TABLES
OF
COMPLEX HYPERBOLIC AND
CIRCULAR FUNCTIONS
BY
A. E. KENNELLY, Sc.D., A.M.
PROFESSOR OF ELECTRICAL ENGINEERING IN HARVARD UNIVERSITY
CAMBRIDGE
HARVARD UNIVERSITY PRESS
LONDON: HUMPHREY MILFORD
Oxford University Press
1914
PHYSICS WBRAft
COPYRIGHT, 1914
BY HARVARD UNIVERSITY PRESS
PHYSICS LIBRARY
PREFACE
The tables in this book present hyperbolic and circular functions of a complex variable,
both in polar and rectangular coordinates. Such complex functions have not hitherto
been published, except over a very restricted range. They have important applications
in electrical engineering. For instance, it is possible with their help to find in a few-
minutes the potential, current and power, at any point of an alternating-current line-
conductor of known constants and terminal conditions; whereas the same problem, to
a like degree of precision, without aid from these functions, and by older methods,
would probably occupy hours of labor and cover several sheets of computing-paper.
Although the principal application of these functions at the present time is in deal-
ing with alternating-current lines, especially those of either great length or high fre-
quency; yet it seems likely that other uses will develop for them.
The author desires to acknowledge his indebtedness, for suggestions and help, to a
number of workers, both in mathematical and practical fields; and particularly to
Messrs. C. L. Bouton, W. Duddell, E. V. Huntington, F. B. Jewett, John Perry, H. J.
Ryan, and E. B. Wilson.
A. E. K.
Harvard University
January, 1914.
fi&zoau
TABLE OF CONTENTS
PAGE
I. Hyperbolic Sines, sinh (p /s) = r [y 2
II. Hyperbolic Cosines, cosh (p [&) = r /_y 8
III. Hyperbolic Tangents, tanh (p [&) = r /_y 14
IV. Correcting Factor. 20
a
V. Correcting Factor. 26
VI. Functions of Semi-Imaginaries. / (p /45 ) 32
VII. Hyperbolic Sines, sinh (x + iq) = u + iv 42
VIII. Hyperbolic Cosines, cosh (x -f iq) = u + iv 58
IX. Hyperbolic Tangents, tanh (x + iq) = u + iv 74
X. Hyperbolic Sines, sinh (x + iq) = r /_y 00
XL Hyperbolic Cosines, cosh (x + iq) = r /_y 106
XII. Hyperbolic Tangents, tanh (x + iq) = r [y_ 122
XIII. Functions of 4 + iq. f (4 + iq) = u + iv 138
/ (4 + iq) = r [y_ 139
gx /e x \
XIV. Semi-Exponentials. - and log 10 \~) J 40
XV. Real Hyperbolic Functions. / (x + io) = u + io 144
XVI. Subdivisions of a Degree 150
Explanatory Text 151
TABLES OF COMPLEX HYPERBOLIC
AND CIRCULAR FUNCTIONS
Table L HYPERBOLIC SINES, sinh (p/5) = r /y
o-3
0.4
0.5
45
O.IOOOO
45.096
0.20000
45.383
0.30001
45.860
0.40005
46.532
0.50016
47-391
46
0.099993
46.095
O.I9995
46.382
0.29985
46.858
0.39968
47.529
0.49944
48.388
47
0.099987
47-95
O.I999O
47.38I
0.29969
47.856
o.3993i
48.526
0.49872
49-385
48
0.099981
48.O94
O.I9986
48.380
0.29954
48.854
0.39893
49.520
0.49799
50.378
49
0.09997s
49.O94
O.I9982
49.378
0.29939
49.852
0.39856
50.513
0.49727
51.368
5
0.099970
50.O94
O.I9976
50.376
0.29923
50.848
0.39820
51-506
0.49656
52.357
5 1
0.099965
5I-093
O.I9972
51-374
0.29907
51.842
0.39784
52-497
0.49585
53-342
52
0.099960
52.092
O.I9968
52-371
0.29892
52.834
0.39748
53-486
0.49514
54-32S
53
0.099955
53-09I
O.I9963
53-367
0.29877
53-826
0.39712
54-472
0-49444
55-304
54
0.099950
54.O9O
O.I9959
54.362
0.29862
54.818
0.39676
55458
0.49374
56.281
55
0.099944
55-089
O.I995S
55-357
0.29847
55-809
0.39641
56.440
0.49305
57-254
56
0.099939
56.088
O.I995I
56.352
0.29833
56.799
0.39607
57-421
0.49238
58.226
57
0.099933
57.086
O.I9946
57-347
0.29819
57.787
0.39572
58.400
0.49172
59-195
58
0.099928
58.085
O.I994I
58.342
0.29804
58.773
o.39538
59-378
0.49106
60.160
59
0.099922
59-083
O.I9937
59-336
0.29790
59.760
0.3950S
60.354
0.49041
61.123
60
0.099917
60.082
O.I9934
60.331
0.29777
60.746
0.39473
61.330
0.48978
62.085
61
O.O999 1 2
6l.o8l
O.I9929
61.324
0.29764
61.731
0.39441
62.302
0.48916
63.042
62
O.O99907
62.079
O.I9925
62.317
0.29751
62.715
0.39409
63.273
0.48855
63.998
63
O.O999O2
63.077
O.I992I
63.309
0.29738
63.698
o.39379
64.243
0.48795
64.950
64
O.O99897
64.075
O.I9918
64.301
0.29725
64.680
o.39349
65.212
0.48738
65.900
65
O.O99893
6 5-073
O.I99I4
65-293
0.29712
65.661
0.39320
66.179
0.48681
66.848
66
O.O99889
66.07I
O.I99 1 1
66.284
0.29700
66.641
0.39293
67.144
0.48627
67.794
67
O.O99885
67.069
O.I9908
67.275
0.29689
67.621
0.39266
68.108
0.4857S
68.738
68
O.O99881
68.066
O.I9904
68.265
0.29678
68.599
0.39240
69.070
0.48523
69.679
69
O.O99877
69.064
O.I99OI
69-255
0.29667
69-577
0.39214
70.030
0.48473
70.617
70
O.O99873
70.062
O.I9898
70.245
0.29657
70.55S
0.39190
70.990
0.48426
71-554
7i
O.O99869
71.059
O.I9895
71-235
0.29647
7L532
0.39167
71.948
0.48380
72.489
72
O.O99865
72.057
O.I9892
72.225
0.29637
72.508
0.39*45
72.905
0.48338
73.422
73
O.O99861
73-054
O.I9889
73-214
0.29628
73-483
0.39123
73-861
0.48296
74-354
74
O.O99858
74-05I
O.I9887
74-203
0.29620
74-458
0.39104
74.817
0.48257
75-284
75
O.O99855
75.048
O.I9885
75-192
0.29612
75-432
0.39084
75-771
0.48220
76.212
76
O.O99852
76.045
O.I9883
76.180
0.29604
76.406
0.39066
76.724
0.48184
77.I38
77
O.O9985O
77.042
O.I9881
77.168
0.29596
77-379
0.39050
77.676
0.48152
78.062
78
O.O99847
78.039
O.I9878
78.156
0.29590
78.351
0.39034
78.628
0.48121
78.986
79
O.O99845
79.O36
O.I9876
79.144
0.28584
79.322
0.39018
79-578
0.48093
79.909
80
O.O99843
80.033
O.I9875
80.131
0.29578
80.294
0.39004
80.528
0.48067
80.830
81
O.O9984I
81.030
O.I9873
81. 118
0.29573
81.266
0.38993
8i.477
0.48044
81.750
82
O.O99839
82.026
O.I9872
82.106
0.29569
82.238
0.38983
82.425
0.48023
82.669
83
O.O99838
83.023
O.I987I
83-093
0.29566
83.209
0.38973
83-373
0.48004
83.587
84
O.O99837
84.020
O.I987O
84.080
0.29563
84.180
0.38965
84.321
0.47987
84-505
85
O.O99836
85.OI7
O.I9869
85.067
0.29561
85.150
0.38958
85.268
0.47972
85.422
86
O.O99835
86.OI4
O.I9868
86.054
0.29559
86.120
0.38952
86.215
0.47960
86.338
87
O.O99834
87.OII
O.I9868
87.041
0.29557
87.090
0.38948
87.162
0.47952
87-254
88
O.O99833
88.008
O.I9867
88.028
0.2955S
88.060
0.38946
88.108
o.47947
88.170
89
O.O99832
89.OO4
O.I9867
89.014
0.29553
89.030
0.38944
89.054
o.47945
89.085
90
O.O9983I
9O.OOO
O.I9867
90.000
0.29552
90.000
0.38942
90.000
o.47943
90.000
Note. sinh (0/8) = o /5.
Examples, sinh (0.3 765 ) = 0.29712 /65.66i =
sinh -1 (0.39018 /79-578) = 0.4 /79
[2]
0.29712 /65.39 , .4o" 1
Table I. HYPERBOLIC SINES, sinh (p [8) - r /y. Continued
0.6
0.7
0.8
9
1.0
o
O
45
46
47
48
49
0.60042 48.440
0.59918 49-437
Q-59793 5-434
0.59667 51.426
0.59542 52-4I4
0.70094 49.676
0.69894 50.679
0.69695 51.676
0.69497 52.666
0.69299 53.652
0.80184 Si-JoS
0.79885 52.112
0.79587 53- io 9
0.79291 54-099
0.78996 55-o82
0.90327
0.89904
0.89482
0.89060
0.88640
52.728
53-735
54-734
55-725
56.707
1.00553
o.99975
0.99394
0.98816
0.98242
54-531
55.546
56-550
57-543
58.525
5
5i
52
53
54
0.59418 53.398
0.59295 54-379
o.59i74 55-355
0-59053 56.326
0.58932 57-293
0.69102 54.632
0.68907 55.606
0.68713 56.574
0.68521 57-537
0.68331 58.493
0.78703 56-058
0.78412 57-026
0.78124 57-987
0.77838 58.940
0-77555 59-886
0.88224
0.87810
0.87400
0.86993
0.86590
57.679
58.642
50-595
60.538
61.472
0.97672
0.97105
0.96543
0.95986
o.95435
59-495
60.453
61.399
62.333
63-255
55
56
57
58
59
0.58814 58.256
0.58698 59.215
0.58583 60.171
0.58469 61.122
0.58357 62.069
0.68144 59.445
0.67959 60.391
0.67776 61.331
0.67595 62.265
0.67419 63.193
0.77275 60.824
0.76999 61.755
0.76727 62.678
0.76459 63.593
0.76195 64.502
0.86192
0.85800
0.85414
0.85034
0.84660
62.396
63.312
64.218
65.114
66.000
0.94890
o.94353
0.93825
0.93305
0.92795
64.166
65.065
65-952
66.827
67.691
60
61
62
63
64
0.58249 63.013
0.58142 63.953
0.58037 64.889
o.57934 65.821
0.57834 66.749
0.67247 64.117
0.67078 65.036
0.66912 65.951
0.66749 66.859
0.66591 67.762
o.75938 6 5-405
0.75686 66.300
0.75439 67.189
0.75197 68.070
0.74962 68.944
0.84295
0.83937
0.83587
0.83244
0.82909
66.878
67-747
68.607
69.458
70.300
0.92295
0.91805
0.91325
0.90856
0.90400
68.544
69-385
70.215
7I-033
71.841
65
66
67
68
69
o.57737 67.674
0.57643 68.596
o.57553 69.515
0.57465 70.430
0-57379 71-342
0.66437 68.661
0.66288 69.554
0.66145 70.444
0.66005 71.329
0.65870 72.209
o.74733 69.812
0.74512 70-674
0.74298 71.529
0.74091 7 2 -379
0.73891 73-223
0.82585
0.82270
0.81967
0.81672
0.81387
71.136
71.962
72.780
73-59
74-392
0.89957
0.89527
0.891 1 1
0.88708
0.88320
72.637
73-424
74.201
74.968
75-723
70
7i
72
73
74
0.57297 72.251
0.57219 73-157
o.57U5 74-o6i
0.57074 74-962
0.57006 75.860
0.65740 73.085
0.65616 73.957
0.65498 74.825
0.65385 75-689
0.65278 76.550
0.73698 74-061
o.735!3 74-894
0-73337 75-722
0.73169 76.544
0.73009 77-36i
0.81114
0.80853
0.80602
0.80363
0.80137
75-i87
75-975
76-756
77-530
78.298
0.87947
0.87589
0.87247
0.86921
0.86612
76.469
77.207
77-936
78.656
79.368
75
76
77
78
79
0.56941 76.756
0.56881 77.649
0.56824 78.540
0.56772 79.429
0.56724 80.317
0.65176 77.408
0.65081 78.263
0.64992 79.114
0.64909 79.962
0.64832 80.808
0.72858 78-I74
0.72716 78.982
0.72583 79-787
0.72459 80.588
0.72345 81.385
0.79924
0.79723
0.79535
0.79359
0.79197
79-59
79-8i5
80.566
81.312
82.053
0.86320
0.86045
0.85788
0.85549
0.85328
80.072
80.769
81.458
82.141
82.818
80
81
82
83
84
0.56679 81.203
0.56638 82.087
0.56602 82.970
0.56570 83.852
0.56542 84.732
0.64761 81.652
0.64697 82.493
0.64640 83.332
0.64589 84.169
0.64545 85.005
0.72241 82.179
0.72146 82.969
0.72061 83.757
0.71985 84-543
0.71919 85.327
0.79048 82.789
0.78913 83.522
0.78792-84-251
0.78685 ,.84.976
0.78592 85.699
0.85125
0.84940
0.84774
0.84628
0.84501
83.489
84.156
-84.817
-85-474
86.128
85
86
87
88
89
0.56518 85.612
0.56498 86.490
0.56483 87.368
0.56473 88.246
0.56466 89.123
0.64507 85.839
0.64476 86.673
0.64452 87.506
0.64435 88.338
0.64425 89.169
0.71863 86.109
0.71817 86.889
0.71781 87.668
0.71755 88.446
0.71740 89.223
0.78513
0.78448
0.78397
0.78361
0.78339
86.420
87.138
87.855
88.571
89.286
0.84393
0.74305
0.84236
0.84186
0.84156
86.779
87.426
88.071
88.715
89.35&
90
0.56464 90.000
0.64422 90.000
0.71736 90.000
0.78333
90.000
0.84147
90.0PQ
Examples, sinh (1
sinh -1
.0 /90 ) = 0.84147
(o.87947 /76.469)
/9-
= 1.0 /7o'
[3]
Table I. HYPERBOLIC SINES, sinh (p [$) r/y. Continued
i-3
1.4
i-S
45
1. 1089
56-5I9
1. 2138
58.692
1-3205
61.034
[.4297
63.568
I-54I8
66.262
46
1.1012
57-543
1.2037
59.726
1.3078
62.092
[.4138
64.639
1.5222
67-355
47
i-935
58.555
I-I937
60.748
1. 2951
63.128
[-3979
65.689
1.5027
68.426
48
1.0858
59-553
1. 1838
6i.753
1.2824
64.142
[.3822
66.717
1.4834
69.474
49
1.0782
60.536
I-I739
62.741
1.2699
65-137
[3665
67.723
1.4642
70.496
50
1.0706
61.506
1.1641
63.712
1-2574
66.113
t-3509
68.707
I-445I
71.492
5i
1.0630
62.461
I-I543
64.666
1.2450
67.068
[-3355
69.668
1.4262
72.462
52
1-0556
63.401
1. 1446
65.603
1.2327
68.004
[.3202
70.605
I-4075
73-405
53
1.0482
64.327
1-1350
66.523
1.2206
68.919
1-3051
7I-5I9
1.3889
74-321
54
1 .0409
65-239
1. 1256
67-425
1.2086
69.814
[.2902
72.409
1.3706
75.210
55
1.0336
66.136
1.1162
68.310
1. 1967
70.688 ]
[2754
73-275
1.3525
76.072
56
1.0265
67.019
1. 1070
69.178
1. 1850
71-542 i
[.2609
74.117
1-3347
76.907
57
1.0195
67.888
1.0979
70.028
I-I735
72.376 ]
[.2466
74-936
1.3172
77.7I3
58
1. 0126
68.742
1 .0890
70.860
1. 1622
73.188 i
[2325
75-730
1.3000
78.491
59
1.0058
69.581
1.0802
7I-675
1.1511
73.980 ]
[.2187
76.500
1. 2831
79.240
60
0.99920
70.406
1.0716
72.474
1. 1403
74-752 l
.2052
77.246
1.2665
79.964
61
0.99269
71.218
1.0632
73-255
1. 1296
75-502 ]
.1919
77.967
1.2503
80.657
62
0.98633
72.016
1.0550
74.019
1.1192
76.232 ]
.1790
78.663
1-2345
81.321
63
0.98013
72.800
1.0470
74.767
1.1091
76.942 ]
.1664
79-335
1.2191
81.956
64
0.97409
73-57Q
1.0392
75-497
1.0992
77.632 ]
.1541
79-983
1.2040
82.562
65
0.96821
74-327
1.0316
76.211
1.0895
78.301 1
.1421
80.607
1. 1894
83.140
66
0.96251
75-07I
1.0242
76.909
1.0802
78.950 !
1305
81.207
1. 1752
83.690
67
0.95698
75-8oi
1.0171
77-590
1.0712
79.580 ]
"93
81.783
1.1615
84.211
68
0.95165
76.519
1.0102
78.257
1.0625
80.191 ]
.1084
82.335
1. 1482
84.704
69
0.94650
77.225
1.0035
78.907
1.0540
80.783 ]
0979
82.865
1. 1354
85.169
70
0.94156
77.918
0.99712
79-543
1.0459
81.357 1
.0879
83-373
1.1231
85.607
7i
0.93682
78.600
0.99099
80.164
1.0382
81.912 1
.0783
83.858
1.1113
86.018
72
0.93229
79.271
0.98514
80.771
1.0308
82.450 ]
.0691
84.322
1. 1000
86.402
73
0.92798
79-931
0-97957
81.365
1.0237
82.971 ]
.0603
84.765
1.0893
86.761
74
0.92388
80.580
0.97428
81.946
1.0170
83.476 ]
.0520
85.188
1.0791
87.096
75
0.92001
81.220
0.96927
82.514
1.0107
83.966 ]
.0441
85.59I
1.0694
87.406
76
0.91637
81.850
0.96456
83.069
1.0047
84.440 ]
0367
85-975
1.0603
87.693
77
0.91296
82.471
0.96015
83.614
0.99916
84.900 ]
.0298
86.342
1.0518
87-9S8
78
0.90978 83.084
0.95605
84.148
0.99397
85.346 1
0233
86.692
1.0439
88.201
79
0.90685
83.689
0.95226
84.672
0.98917
85.780 ]
oi73
87.026
1.0366
88.425
80
0.90416
84.286
0.94878
85.187
0.98477
86.202 ]
.0119
87.346
1.0299
88.630
81
0.90172
84.877
0.94562
85.693
0.98077
86.614 ]
.0069
87.651
1.0238
88.818
82
0.89953
85.462
0.94279
86.191
0.97715
87.016 ]
.0024
87.944
1.0183
88.991
83
0.89759
86.041
0.94029
86.683
0.97400
87.408 c
>-99845
88.227
1-0135
89.149
84
0.89590
86.616
0.9381 1
87.169
0.97124
87-793 <
)-99502
88.499
1.0093
89.294
85
0.89447
87.186
0.93626
87.649
0.96890
88.171 c
>.992io
88.762
1.0057
89.429
86
0.89330 87.753
o.93474
88.124
0.96698
88.544 c
).9897i
89.018
1.0027
89-554
87
0.89238
88.317
o.93356
88.596
0.96548
88.912 c
>-98785
89.269
1 .0004
89.673
88
0.89173
88.879
0.93272
89.065
0.96441
89.277 c
>.98652
89-515
0.99880
89.785
89
0.89134
89.440
0.93221
89-533
0.96377
89.639 c
>-98572
89.758
0.99782
89.893
90
0.891 2 1
90.000
0.93204
90.000
0.96356
90.000 c
>.98545
90.000
0.99749
90.000
Examples
sinh (1
I/4J!) =
1. 1089 /
56\si9 = 1
.io89/56.3i'.o8
sinh -1 (
1. 1084/8
2 -335) =
1.4 /68.
[4]
Table I. HYPERBOLIC SINES, sinh (p /5) = r fa Continued
1.6
i-7
1.8
1.9
45
1-6575
69.117
1.7776
72.I33
1.9029
75.292
2.0343
78.590
2.1726
82.016
46
1.6338
70.241
1-7493
73-288
1-8693
76.486
1.9947
79.829
2.1266
83304
47
1. 6103
71-339
1. 7210
74.418
1-8359
77-65I
1-9554
81.037
2.0809
84.560
48
1.5868
72.409
1.6929
75-5I5
1.8027
78.784
1-9165
82.210
2.0356
85-778
49
I-5635
73-451
1.6651
76.582
1.7697
79.883
1.8779
83.346
1.9907
86.958
50
1.5404
74-46S
1-6375
77.618
1.7370
80.946
1.8396
84.444
1.9462
88.098
Si
I-5I75
75-449
1.6102
78.620
1.7046
81.974
1.8016
85-503
1.9022
89.196
52
1.4949
76.402
1-5831
79-590
1.6726
82.966
I-7643
86.524
1.8588
90-253
53
1-4725
77-325
I-5563
80.527
1.6410
83.921
1.7273
87-505
1.8160
91.267
54
1.4504
78.218
I-5299
81.429
1.6098
84.839
1 .6909
88.444
1-7737
92.236
55
1.4285
79.079
1-5039
82.296
I-579I
85.718
1-6550
89.342
1.7320
93.160
56
1.4070
79.910
1.4782
83.128
1.5488
86.558
1.6196
90.197
1.6911
94.039
57
1-3859
80.709
I-4530
83.924
1-5190
87-358
1.5848
91.008
1.6509
94.869
58
1-3651
81-475
1.4282
84.683
1.4898
88.116
1.5506
91-773
1.6114
95-65o
59
1-3447
82.209
1.4039
85.406
1.4611
88.834
I-5I7I
92-493
1.5726
96.382
60
I-3247
82.910
1.3800
86.091
I-4330
89.510
1.4843
93.167
1-5347
97.062
61
1-3051
83-578
I.3567
86.738
1-4055
90.142
1.4523
93.792
1.4976
97.688
62
1.2860
84.212
1-3339
87-347
I-3787
90.730
1.4210
94.368
1. 46 14
98.261
63
1.2674
84.813
1.3117
87.917
I-3525
91.274
I-3904
94.893
1.4260
98.778
64
1.2492
85-380
1. 2901
88.447
1.3270
91-774
1.3606
95-368
I-39I5
99.238
65
1. 2316
85-9I3
1.2690
88.938
1.3022
92.228
i-33 l6
95-792
1.3580
99.639
66
1. 2145
86.413
1.2486
89.390
1. 2781
92.636
1-3035
96.162
I.3255
99.980
*7
I-I979
86.879
1.2288
89.802
1.2548
92.997
1.2762
96.478
1.2940
100.261
68
1.1819
87.311
1.2097
9 - x 75
1.2322
93-312
1.2499
96.741
1.2635
100.479
69
1. 1664
87.710
1.1913
90.508
1. 2104
93-58o
1.2244
96.949
1.2340
100.634
70
1.1516
88.076
1-1736
90.801
1.1895
93.802
1. 1999
97.102
1.2056
100.725
7i
I-I373
88.410
1.1566
9 x -055
1. 1694
93.976
1-1764
97.199
1-1783
100.750
72
1-1237
88.712
1-1403
91.271
1-1502
94.104
1. 1539
97.241
1.1521
100.709
73
1.1107
88.982
1. 1248
91.448
1.1318
94.187
1-1324
97.227
1.1271
100.602
74
1.0984
89.221
I. HOI
91.588
1. 1 144
94.224
1.1119
97-I58
1.1033
100.428
75.
1.0867
89.431
I. O96 1
91.692
1.0979
94.215
1.0925
97-034
1.0807
100.187
76
I-Q757
89.613
I.0829
91.760
1.0823
94.162
1 -0743
96.856
1-0594
99.880
77
1.0654
89.767
I.O706
9J-794
1.0677
94.068
1-0571
96.625
1.0394
99-507
78
1-0558
89.894
1. 059 1
9J-795
1-0541
93-933 '
1.0411
96-343
1.0207
99.070
79
1.0469
89.997
I.O485
9I-765
1. 0415
93-758
1.0262
96.012
1.0033
98-57I
80
1.0388
90.076
I.O388
91-705
1.0299
93-545
1.0126
95-633
0.98729
98.011
81
1-0314
90-!34
I.O299
91.618
1.0194
93.298
1.0002
95.209
0.97271
97-394
82
1.0248
90.171
I.02I9
9i-5o5
1.0099
93.019
0.98899
94-744
0.95958
96.722
83
1.0189
90.191
I. OI49
91.370
1.0015
92.711
0.97907
94.240
0.94792
96.000
84
1.0138
90.194
I.0088
91.214
0.99422
92-374
0.97043
93.702
0-93775
95-233
85
1.0095
90.184
I.OO36
91.039
0.98802
92.015
0.96309
93-133
0.92911
94.426
86
1 .0060
90.161
O.99929
90.850
0.98293
91.636
0.95706
92-539
0.92201
93-584
87
1.0032
90.129
O.99596
90.649
0.97896
91.241
0.95236
9!-9 2 3
0.91646
92.713
88
1.0012
90.090
0.99357
90.438
0.97612
90.834
0.94899
91.291
0.91248
91.821
89
1. 0000
90.046
O.992I4
90.220
o.97442
90.419
0.94697
90.648
0.91009
90.914
90
0-99957
90.000
O.99166
90.000
0.97385
90.000
0.94630
90.000
0.90930
90.000
Examples
. sinh (
[.6 /6o)
= 1-3247
/82.9io
= 1.3247
/82.54'.
*6".
sinh -1
(1.IQ99 /97-io2)
= 1.9 /70
[5]
Table I. HYPERBOLIC SINES, sinh (p [$) = r [y. Continued
2.1 2.2 2.3 2.4 2.5
00 o o o o
45 2.3190 85.558 2.4745 89.205 2.6404 92.946 2.8177 96.769 3.0079 100.661
46 2.2658 86.905 2.4135 90.613 2.5707 94419 2.7386 98.312 2.9185 102.278
47 2.2131 88.213 2.3530 91.981 2.5017 95-85 1 2.6603 99-813 2.8301 103.852
48 2.1608 89.482 2.2930 93.307 2.4334 97-241 2.5829 101.271 2.7429 105.383
49 2.1090 90.711 2.2337 94.592 2.3659 98.588 2.5065 102.685 2.6568 106.869
50 2.0577 91.898 2.1750 95-834 2.2992 99.890 2.4311 104.053 2.5720 108.309
51 2.0071 93.042 2.1171 97-031 2.2334 101.146 2.3568 105.375 2.4885 109.701
52 1.9571 94.142 2.0600 98.181 2.1685 102.354 2.2836 106.648 2.4064 111.044
53 1.9078 95.197 2.0037 99.284 2.1046 103.514 2.2117 107.871 2.3257 112.337
54 1.8592 96.205 1.9483 100.338 2.0418 104.623 2.1410 109.042 2.2465 113.578
55 1.8114 97.165 1.8938 101.342 1.9801 105.680 2.0714 110.160 2.1687 114.765
56 1.7644 98.076 1.8402 102.294 1.9195 106.683 2.0032 in. 223 2.0925 115.896
57 1. 7182 98.935 1.7876 103.193 1.8600 107.629 1.9364 112.228 2.0178 116.970
58 1.6729 99.742 1.7360 104.035 1. 8016 108.518 1.8709 113. 174 1-9447 117.984
59 1.6284 100.494 1.6854 104.820 1.7445 109.347 1.8068 114.059 1-8733 118.936
60 1.5849 101.191 1.6359 105.546 1.6886 110.114 1. 7441 114.880 1.8035 119.823
61 1.5424 101.830 1.5875 106.216 1.6340 110.816 1.6829 115.634 1-7353 120.642
62 1.5008 102.410 1.5402 106.811 1.5807 in. 451 1.6232 116.319 1.6688 121. 391
63 1.4603 102.929 1.4941 107.345 1.5287 112.016 1.5649 116.931 1.6040 122.067
64 1.4208 103.386 1.4492 107. 811 1.4780 112.509 1. 5081 117.467 1.5409 122.665
65 1.3824 103.777 1.4055 108.207 1.4286 112.926 1.4528 117.924 1.4794 123.182
66 1-3451 104.101 1.3630 108.529 1.3806 113.264 1.3991 118.297 1.4196 123.613
67 1.3089 104.357 1 3218 108.775 1.3341 113-519 I-3469 118.583 1.3616 123.954
68 1.2738 104.542 1. 2819 108.943 1.2890 113.688 1.2963 118.777 1-3052 124.198
69 1.2399 104.655 1.2433 109.029 1.2453 113-767 1-2473 118.874 1.2506 124.341
70 1.2072 104.694 1.2060 109.030 1. 2031 113.752 1. 1999 118.868 1. 1977 124.376
71 1.1758 104.656 1.1701 108.944 1. 1624 113.638 1.1541 118.754 1. 1466 124.296
72 1. 1457 104.541 1.1356 108.769 1. 1232 113.422 1. 1099 118.526 1.0972 124.092
73 1.1168 104.348 1. 1026 108.501 1.0857 113. 100 1.0675 118.177 1.0497 123.755
74 1.0893 104.074 1.0711 108.138 1.0498 112.667 1.0268 117.701 1.0040 123.277
75 1.0632 103.719 1.0411 107.678 1.0155 112. 118 0.98795 117.091 0.96019 122.648
76 1.0385 103.283 1.0126 107. 119 0.98292 111.449 0.95090 116.341 0.91831 121.857
77 1-0153 102.766 0.98581 106.459 0.95214 110.659 0.91576 115.443 0.87843 120.891
78 0.99353 102.168 0.96065 105.699 0.92320 109.744 0.88261 114.390 0.84063 119.740
79 0.97332 101.491 0.93722 104.839 0.89615 108.701 0.85152 113. 178 0.80503 118.392
80 0.95468 100.736 0.91557 103.879 .0.87109 107.531 0.82256 111.803 0.77173 116.836
81 0.93765 99907 0.89575 102.822 0.84808 106.233 0:79589 110.261 0.74083 115.063
82 0.92229 99.008 087784 101.671 0.82719 104.810 0.77158 108.550 0.71251 113.065
83 0.90862 98.043 0.86187 100.432 0.80853 103.267 0.74974 106.676 0.68692 110.841
84 0.89668 97.015 0.84789 99. in 0.79215 101.611 0.73051 104.643 0.66422 108.390
85 0.88652 95.933 0.83596 97.715 0.77813 99.851 0.71396 102.462 0.64461 105.723
86 . 0.87817 94.806 0.82613 96.254 0.76655 98.000 0.70026 100.147 0.62827 102.855
87 0.87164 93.639 0.81845 94.740 0.75747 96.071 0.68948 97.717 0.61536 99.811
88 0.86696 92.443 0.81293 93.183 0.75095 94.082 0.68171 95.197 0.60602 96.624
89 0.86414 91.226 0.80961 91.599 0.74702 92.051 0.67703 92.615 0.60036 93.338
90 0.86321 90.000 0.80850 90.000 0.74571 90.000 0.67546 90.000 0.59847 90.000
Examples, sinh (2.5 /75 = 0.96019 /i22,648 = 0.96019 /i22.38'.53 l> .
sinh" 1 (0.60036 /93-338) = 2.5 /J\
[6]
Table I. HYPERBOLIC SINES, sinh (p [$) -.-r/y. Continued
2.6
2.7
2.8
2.9
3-o
45
3.2121
104.613
34318
108.614
3-6685
112.653
3.9236
116. 721
4.1986
[20.814
46
3-i"5
106.307
3-3 J 9i
110.386
3-5426
114.506
3-7832
118.658
4.0426
[22.832
47
3.0123
107.957
3.2079
112. 116
3-4186
116.317
3.6453
120.551
3-8895
[24.808
48
2.9144
109.564
3-0985
1 13.801
3.2966
118.084
3-5098
122.400
3-7394
[26.741
49
2.8179
in. 126
2.9908
115.442
3.1767
119.806
3-3768
124.205
3-5923 :
[28.630
50
2.7229
1 1 2.641
2.8849
117.037
3-0590
121.483
3-2465
125.965
3-4483 3
[30.474
5i
2.6295
114.109
2.7809
118.585
2.9436
123. 113
3-1189
127.679
3.3076 :
[32.272
52
2.5378
115-528
2.6789
120.084
2.8306
124.694
2.9941
129.345
3-i7oi ]
[34.024
S3
2.4478
116.897
2.5789
121.532
2.7200
126.226
2.8721
130.963
3-0359 1
[35.729
54
2-3595
118. 214
2.4809
122.929
2.6118
127.708
2.7529
132.532
2.9051 ]
[37.386
55
2.2729
119.476
2.3850
124.274
2.5060
129.138
2.6366
134.050
2.7777 3
[38.994
56
2.1882
120.684
2.2913
125.563
2.4027
130.515
2.5232
I35-5I7
2.6536 ]
[40.553
57
2.1053
121.834
2.1996
126.797
2.3019
131-837
2.4127
136.932
2.5330 1
[42.062
58
2.0242
122.925
2.1101
127.973
2.2036
133-103
2-3051
138.293
2.4157 ]
[43.5I9
59
1-945
123-954
2.0228
129.088
2.1077
134-3"
2.2004
I39-598
2.3018 ]
[44.924
60
1.8677
124.918
1-9377
130.140
2.0144
135-459
2.0986
140.847
2.I9I2 ]
[46.276
61
1-7923
125.816
1.8547
131. 128
1.9236
I36-544
1.9997
142.037
2.0839 .
[47-574
62
1.7187
126.644
1-7739
132.047
1.8352
I37-565
1.9036
143.167
I.9798 ]
[48.817
63
1.6470
127.399
1.6952
132.895
1-7493
138.519
1.8103
144-235
I.8789 ]
[50.OO4
64
1-5772
128.077
1.6187
133.669
1.6658
I39-403
1.7198
I45.239
1. 7812 ]
'51-133
65
1.5094
128.674
1.5442
134-364
I-5847
140.214
1-6319
146.176
I.6865 ]
[52.204
66
1-4435
129.185
1.4719
134.978
1.5060
140.948
1-5467
147.044
I.5948
[53.2I4
67
1-3794
129.606
1.4016
135-504
1-4295
141.599
1. 4641
147.838
1. 506 1 1
[54.161
68
1.3171
129.930
1-3334
135-935
1-3553
142.164
1.3840
148.555
I.4202
[55.043
69
1.2568
130.151
1.2673
i3"6.266
1-2833
142.634
1.3063
149.190
I-3370
[55.858
70
1. 1983
130.262
1. 2031
136.489
1. 2136
143.005
1. 2310
149.738
1.2565
[56.602
7i
1.1417
130-254
1. 1409
136.596
1. 1460
143.267
1.1581
150.191
1. 1785 I
[57.271
72
1.0870
130-117
1.0807
136.576
1.0804
143.411
1.0874
150.541
I. IO3O ]
[57.860
73
1-0341
129.841
1.0226
136-415
1.0169
143.424
1. 01 89
150.780
I.O298 ]
[58.363
74
0.98316
129.414
0.96631
136. 101
o.9555o
143.292
0.95251
150.894
O.95893 ]
[58.772
75
0.93420
128.822
0.91207
135-617
0.89606
142.996
0.88819
150.867
O.89O22 3
59-077
76
0.88720
128.049
0.85985
134-943
0.83862
142.516
0.82587
150.680
O.82356 ]
59-265
77
0.84227
127.079
0.80965
134.058
0.78319
141.827
0.76551
150.309
0.75887 1
59-3I9
78
0.79948
125.893
0.76157
I32.935
0.72979
140.897
0.70706
149.721
O.69605 3
[59.216
79
0.75891
124.471
0.71568
i3 I -542
0.67847
139.686
0.65054
148.876
O.63503 ]
[58.925
80
0.72068
122.793
0.67215
129.847
0.62934
138.145
0.59597
147.721
C57573 3
58.404
81
0.68499
120.837
0.63109
127.812
0.58252
136.217
o.5434o
146.183
O.51809 ]
57-592
82
0.65203
118.583
o.59275
125.396
0.53822
133-833
0.49294
144.169
O.46213 3
56.404
83
0.62196
116. 016
0-55739
122.554
0.49674
130.908
0.44484
141-553
O.40789 ]
[54.709
84
0.59507
113. 126
0.52536
119.252
0.45849
127.351
0.39946
138.168
0.35548 3
[S 2 ^
85
0.57164
109.910
0.49705
115-458
0.42399
123.066
o.35738
133-795
O.3O52I ]
[48-903
86
0.55191
106.382
0.47291
1 1 1. 164
o.39394
117.968
0.31946
128.168
0.25775 3
[43-974
87
0.53621
102.571
0.45344
106.390
0.36915
112.015
0.28691
121.005
C2I433 "
[36.701
88
0.52479
98.524
0.43912
101.194
0.35055
105.244
0.26143
112. no
O.1773I 3
[25-843
89
0.51783
94.307
0.43033
95.682
0.33893
97.809
0.24496
101.576
O.15092
[10.091
90 0.51550 90.000 0.42738 90.000 0.33499 90.000 0.23925 90.000 0.14112 90.000
Examples, sinh (3.0 /50 ) = 3-4483 /i3Q-474 = 3-4483 /i3Q .28'.26*.
sinh -1 (0.15092 /iio.09i) = 3.0 /89 .
[7]
Table II. HYPERBOLIC COSINES, cosh (p [8) = r [y
-3
0.4
o-S
45
1. 0000 1
0.287
1. 0001 3
1. 148
1.00067
2.578
1.00210
4-578
1.00519
7-I4I
46
0.99983
0.287
o.99943
1. 146
0.99910
2-577
0-99933
4-584
1.00085
7-159
47
0.99966
0.286
0.99873
1. 144
0-99753
2.576
0.99655
4-584
0.99649
7.166
48
0.99948
0.285
0.99804
1. 141
o.99597
2.571
0.99378
4-578
0.99214
7-165
49
0.99931
0.283
0-99735
1. 136
o.9944i
2.562
0.99101
4-566
0.98780
7-155
5
0.99914
0.282
0.99666
1. 131
0.99285
2.551
0.98824
4-551
0.98347
7-137
Si
0.99897
0.280
o.99597
1. 123
0.99131
2-536
0.98547
4.528
0.97917
7.109
52
0.99880
0.278
0.99529
1. us
0.98977
2.519
0.98274
4.500
0.97490
7-o73
53
0.99863
0.275
0.99462
1. 105
0.98825
2.498
0.98003
4.467
0.97065
7.028
54
0.99846
0.272
0-99395
1.094
0.98674
2-474
o.97734
4.427
0.96644
6-973
55
0.99830
0.269
0.99329
1. 081
0.98525
2.447
0.97468
4.382
0.96226
6.910
56
0.99814
0.265
0.99263
1.067
0.98377
2.417
0.97205
4-332
0.95814
6.838
57
0.99798
0.261
0.99199
1.052
0.98232
2-383
0.96945
4.276
0.95406
6.756
58
0.99782
0.257
o.99i35
1.036
0.98089
2-347
0.96690
4.214
0.95005
6.666
59
0.99766
0-253
0.99073
1.018
0.97948
2.308
0.96438
4-147
0.94609
6.567
60
0.99751
0.249
0.99012
o.999
0.97810
2.267
0.96191
4-075
0.94219
6.460
61
0.99736
0.244
0.98952
o.979
0.97674
2.221
0.95948
3-998
0.93838
6-343
62
0.99721
0.238
0.98893
o-957
o.9754i
2.173
0-9S7H
3-914
0.93465
6.217
63
0.99707
0.232
0.98835
o.934
0.97411
2.123
0.85478
3-826
093099
6.083
64
0.99693
0.226
0.98780
0.910
0.97285
2.070
0-95251
3-733
0.92741
5-941
65
0.99679
0.220
0.98725
0.885
0.97163
2.014
0.95031
3-63S
o.92393
5-789
66
0.99666
0.214
0.98672
0.859
0.97044
1-955
0.94816
3-532
0.92054
5631
67
0.99653
0.207
0.98621
0.832
0.96927
1.894
0.94608
3-423
0.91725
5-463
68
0.99641
0.200
0.98571
0.804
0.96814
1.830
0.94407
3-3io
0.91407
5-288
69
0.99629
0.193
0.98523
0-775
0.96706
1.764
0.94213
3-193
0.91 100
5.106
70
0.99617
0.185
0.98477
o.744
0.96601
1.696
0.94026
3.072
0.90805
4.916
7i
0.99606
0.177
0.98433
0.713
0.96500
1.626
0.93846
2.946
0.90521
4.718
72
0.99596
0.169
0.98391
0.681
0.96404
1-553
0.93674
2.816
0.90248
4.5I3
73
0.99586
0.161
0.98350
0.648
0.96313
1.479
0.93510
2.682
0.89989
4.302
74
0.99576
O.I53
0.98312
0.614
0.96227
1.402
0-93354
2-544
0.89742
4.085
75
0.99567
0.144
0.98276
0.580
0.96145
1.324
0.93207
2.403
0.89508
3-86i
76
0-99559
0.13S
0.98242
0-545
0.96068
1.244
0.93069
2.258
0.89288
3-631
77
o.9955i
0.126
0.98210
0.509
0.95996
1. 162
0.92938
2. in
0.89081
3-396
78
0.99544
0.1 17
0.98181
0.472
095929
1.078
0.92816
1.960
0.88889
3-155
79
0-99537
0.108
0.98154
0-435
0.95866
0-993
0.92705
1.807
0.8871 1
2.910
80
o.9953i
0.099
0.98128
o.397
0.95808
0.908
0.92603
1.652
0.88548
2.660
81
0.99525
0.090
0.98105
o-359
0.95756
0.821
0.92509
1.494
0.88399
2.406
82
0.99520
0.080
0.98085
0.320
0.95710
0.732
0.92425
1-333
0.88266
2.149
83
o.995i5
0.070
0.98067
0.281
0.95670
0.643
0.62351
1. 1 70
0.88147
1.888
84
0.995 1 1
0.060
0.98051
0.242
0.95635
0-5S2
0.92287
1.006
0.88044
1.624
85
0.99508
0.050
0.98037
0.203
0.95605
0.461
0.92233
0.841
0.87957
1-357
86
0.99506
0.040
0.98026
0.163
0.95580
0.369
0.92189
0.675
0.87886
1.087
87
0.99504
0.030
0.98018
0.123
0.95560
0.277
0.92154
0.508
0.87830
0.816
88
0.99502
0.020
0.98012
0.082
0.85545
0.185
0.92128
0.340
0.87790
o.544
89
0.99501
O.OIO
0.98009
0.041
0-95537
0.093
0.921 12
0.171
0.87766
0.272
90
0.99500
0.000
0.98007
0.000
0-95534
0.000
0.92106
0.000
0.87758
0.000
Note. cosh (o/3) = 1.0 /o for all values of 5.
Examples, cosh (0.5 /8i ) = 0.88399 /2.4o6 = 0.88399 /2.24 , .22*
cosh * (0.97810 /2.26y) = 0.3 /6o.
[8]
Table II. HYPERBOLIC COSINES, cosh (p [S) - r /y. Continued
0.6
0.7
0.8
0.9
45
1.01070
10.254
1.01982
13.890
1.03360
18.010
1-05333
22.567
1.08031 27.487
46
1.00449
10.291
1.01136
13.960
1.02263
18.132
1-03959
22.755
1.06358 27.762
47
0.99825
10.315
1.00289
14.013
1.01164
18.231
1.02583
22.919
1.04680 28.011
48
0.99199
10.327
0.99441
14.050
1.00063
18.309
1. 01 203
23-059
1.03000 28.235
49
0.98575
10.326
0.98594
14.071
0.98963
18.368
0.99822
23.176
1. 013 1 5 28.433
5
Q-97953
10.313
0.97748
14.075
0.97864
18.405
0.98443
23.267
0.99632 28.603
5i
Q-97333
10.287
0.96906
14.061
0.96768
18.421
0.97064
23-332
0.97950 28.743
52
0.96716
10.248
0.96066
14.031
0.95675
18.414
0.95690
23-372
0.96270 28.854
53
0.96103
10.196
0.95232
13.982
0.94587
18.384
0.94320
23-383
0.94596 28.933
54
Q-95495
10.131
0.94404
13.916
0.93506
18.332
o.92957
23-367
0.92928 28.981
55
0.94893
10.053
0.93582
13-831
0.92432
18.256
0.91603
23.321
0.91267 28.994
56
0.94296
9.961
0.92768
13.728
0.91367
18.156
0.90257
23.246
0.89615 28.974
57
0.93706
9-856
0.91962
13.606
0.90312
18.031
0.88922
23.140
0.87976 28.917
58
0.93125
9-738
0.9 1 1 66
13-465
0.89270
17.881
0.87602
23.003
0.86350 28.823
59
0.92552
9.606
0.90382
13.306
0.88240
I7-705
0.86294
22.833
0.84739 28.689
60
0.91987
9.461
0.89607
13.127
0.87222
17-505
0.85001
22.631
0.83142 28.518
61
0.91433
9-303
0.88846
12.929
0.86221
17.278
0.83727
22.394
0.81564 28.303
62
0.90889
9-I3I
0.88100
12.713
0.85237
17.024
0.82471
22.122
0.80008 28.047
63
0.90357
8.945
0.87369
12.476
0.84271
16.743
0.81237
21.814
0.78475 27.745
64
0.89838
8.747
0.86653
12.220
0.83324
16.435
0.80025
21.471
0.76966 27.396
65
0.89332
8.536
0.85954
"945
0.82398
16.100
0.78837
21.091
0.75484 26.999
66
0.88838
8.312
0.85272
11.652
0.81494
I5.738
0.77675
20.673
0.74029 26.555
67
0.88358
8.076
0.84609
"339
0.80613
15-349
0.76540
20.218
0.72603 26.061
68
0.87894
7.827
0.83966
11.007
0.79757
14-931
o.75435
19.722
0.71212 25.513
69
0.87445
7-565
0.83344
10.656
0.78927
14.486
0.74362
19.188
0.69857 24.911
70
0.87012
7.292
0.82744
10.287
0.78125
14.014
0.73322
18.615
0.68539 24.254
7i
0.86596
7.007
0.82166
9.900
0.77352
I3.5I5
0.72317
18.001
0.67261 23.541
72
0.86197
6.711
0.81611
9.496
0.76610
12.990
0.7I347
I7.348
0.66026 22.772
73
0.85816
6.404
0.81081
9075
0.75899
12.438
0.70416
16.656
0.64836 21.946
74
0.85454
6.086
0.80576
8.637
0.75220
11.860
0.69527
15.926
0.63692 21.061
75
0.851 1 1
5-758
0.80097
8.183
0.74575
11.257
0.68681
I5-I56
0.62599 20.115
76
0.84787
5.420
0.79646
7-713
o.73965
10.630
0.67878
14-347
0.61560 19.111
77
0.84484
5-073
0.79222
7.228
o.73392
9-979
0.67121
13-502
0.60577 18.049
78
0.84201
4.718
0.78826
6.729
0.72856
9.306
0.66412
12.621
0.59652 16.929
79
0.83939
4-355
0.78459
6.217
0.72359
8.612
0.65753
11.706
0.58790 15.753
80
0.83698
3-984
0.78121
5-694
0.71901
7.897
0.65145
io.755
0.57991 14.521
81
0.83479
3.606
0.77814
5-159
0.71484
7.164
0.64589
9.776
0.57259 13-237
82
0.83282
3.221
o.77538
4.613
0.71108
6.413
0.64087 8.768
0.56596 -1 1.904
83
0.83108
2.831
0.77293
4-057
0.70774
5.647
0.63641
_ 7-733
0.56005 .10.526
84
0.82957
2.436
0.77079
3-493
0.70483
4.867
0.63252
6.674
0.55487 9- io 5
85
0.82828
2.037
0.76898
2.922
0.70236
4-075
0.62921
5-595
0.55046 7.647
86
0.82722
1.634
0.76750
2-345
0.70033
3.272
0.62648
4.498
0.54683 6.157
87
0.82640
1.228
0.76634
1.763
0.69875
2.462
0.62435
3-386
0.54399 4.642
88
0.82581
0.820
0.76551
1. 177
0.69761
1.645
0.62283
2.263
0.54195 3-io6
89
0.82546
0.410
0.76501
0.589
0.69693
0.823
0.62192
i-i33
0.54072 1.556
90
0.82534
0.000
0.76484
0.000
0.69671
0.000
0.62161
0.000
0.54030 0.000
Examples, cosh
a-7 /7i)
= 0.82166 /9.9QO
= 0.82166 /9.54'.<
30 .
cosh l
(0.60857 /24.9")
= 1.0/69 .
[9]
Table II. HYPERBOLIC COSINES, cosh (p [S) - r fa Continued
i-3
1.4
i-5
45
I-H57
32.686
1. 1608
38.076
1. 2163
43-57o
1.2830
49.084
1. 3616
54-5SO
46
1.0959
33-o67
1-1376
38.582
1. 1897
44.210
1.2529
49.864
1-3279
55-471
47
I-Q759
33-424
1.1143
39.063
1. 1630
44.827
1.2227
50.625
1. 2941
56.378
48
I-Q559
33-754
1. 0910
39.5I7
1-1363
45-421
1. 1926
5I-365
1.2604
57.266
49
1 -359
34-056
1.0676
39-943
1-1095
45.989
1. 1624
52-083
1.2267
58.134
5
1.0158
34-328
1.0443
40.341
1.0828
46.529
1. 1322
52-777
1.1931
58.982
Si
0.99578
34-57Q
1.0209
40.709
1. 0561
47.041
1.1021
53-446
1.1596
59.810
52
o.97577
34.780
0-99757
41-045
1.0294
47-525
1.0720
54.090
1. 1262
60.618
53
0.95580
34-957
0.97428
41-349
1.0027
47-978
1.042 1
54.708
1.0929
61.407
54
0-93589
35- I oo
0.95104
41.618
0.97613
48.400
1.0122
55-299
1.0598
62.175
55
0.91605
35.206
0.92788
41.850
0.94964
48.788
0.98242
55.862
1.0268
62.921
56
0.89630
35-275
0.90481
42.045
0.92325
49.141
0.95277
56.396
0.99406
63-645
57
0.87666
35-305
0.88186
42.201
0.89697
49.458
0.92327
56.900
0.96149
64-347
58
0.85716
35-293
0.85902
42.314
0.87082
49-736
0-89393
57-372
0.92912
65025
59
0.83781
35-238
0.83633
42.383
0.84482
49-973
0.86474
57.811
0.89696
65.681
60
0.81862
35-139
0.81379
42.406
0.81898
50.168
0-83573
58.214
0.86502
66.313
61
0.79961
34.992
0.79144
42.379
o.7933i
50.315
0.80692
58.578
0.83332
66.919
62
0.78081
34-794
0.76929
42.299
0.76783
50.412
0.77831
58.902
0.80186
67.497
63
0.76223
34-545
0-7473S
42.164
0.74256
50.457
0.74991
59-i85
0.77065
68.048
64
0.74390
34.242
0.72565
41.970
0.71752
50.446
0.72173
59-421
0.73969
68.571
65
0.72584
33-881
0.70420
41-713
0.69271
50.373
0.69377
59.608
0.70899
69.064
66
0.70808
33-459
0.68304
41.389
0.66815
50.235
0.66605
59-742
0.67855
69.524
67
0.69063
32.974
0.66218
40.993
0.64385
50.026
0.63858
59-8i7
0.64836
69.950
68
0.67352
32.423
0.64164
40.520
0.61985
49-739
0.61136
59.828
0.61844
70.340
69
0.65677
31.804
0.62146
39.966
0.59618
49.368
0.58441
59-769
0.58877
70.689
70
0.64043
31. 112
0.60166
39-324
0.57283
48.905
o.55775
59.633
0-55937
70.995
7i
0.62452
30.344
0.58227
38.589
0.54984
48.342
o.53i37
59.410
0.53022
71.253
72
0.60907
29.498
0.56334
37-754
0.52724
47.668
0.50529
59.090
0.50134
7I.458
73
0.59410
28.570
0.54489
36.812
0.50506
46.870
0-47955
58.659
0.47271
71.602
74
0.57966
27.558
0.52697
35-756
0.48335
45-937
0.45414
58.104
o.44434
71.677
75
0.56579
26.458
0.50963
34.578
0.46215
44.856
0.42910
57.405
0.41622
71.672
76
0.55252
25.269
0.49292
33-271
0.441 5 1
43.610
0.40446
56.542
0.38836
71-573
77
0-53990
23.989
0.47688
31.828
0.42149
42.180
0.38028
55487
0.36075
71.361
78
0.52796
22.616
0.46159
30.242
0.40216
40.548
0.35658
54.206
0-33339
71.015
79
0.51675
21. 151
0.44710
28.507
0.38360
38.692
0-33345
52.659
0.30630
70.501
80
0.50631
19-594
0-43349
26.616
0.36591
36.591
0.31099
50.800
0.27951
69.774
81
0.49669
17.946
0.42083
24.567
0.34921
34-223
0.28928
48.566
0.25304
68.774
82
0.48794
16.210
0.40919
22-359
0.33362
31-569
0.26848
45.888
0.22691
67413
83
0.48009
14-391
0.39867
19-993
0.31928
28.608
0.24877
42.681
0.20122
65-561
84
0.47320
12.495
0-38935
17-475
0.30635
25-333
0.23039
38.853
0.17608
63.018
85
0.46730
10.529
0.38129
14.813
0.29499
21.739
0.21368
34303
0.15169
59-474
86
0.46241
8.501
o.37457
12.022
0.28538
17.838
0.19902
28.949
0.12853
54.420
87
0.45857
6.422
0.36927
9.121
0.27770
I3-659
0.18684
22.746
0.107 10
47.029
88
0.45581
4-304
0.36545
6.132
0.27208
9.247
0.17765
15-729
0.08871
36.059
89
o.4S4i5
2-159
0.36314
3-o8i
0.26865
4.668
0.17193
8.051
0.07570
20.198
90
0.45360
0.000
0.36236
0.000
0.26750
0.000
0.16997
0.000
0.07074
0.000
Examples.
cosh (1.
3/73) =
= 0.50506 /46.87o
= 0.50506 /46.52'
.12*.
cosh -1 (
0.07074 /o) = 1.5
/90-
[10]
Table II. HYPERBOLIC COSINES, cosh (p [$) = r /t. Continued
1.6
i-7
1.8
1.9
45
1.4524
59.916
1-5556
65.149
1.6714
70.229
1.7999
75.I52
I-94I3
79.922
46
I-4H9
60.974
1.5141
66.336
1.6257
7I-536
1.7496
76.569
1.8861
8i.437
47
1-3774
62.021
1.4727
67.516
1.5802
72.837
1.6997
77.979
1-8313
82.947
48
1.3400
63-051
1.4316
68.681
I-535Q
74-125
1.6502
79-378
1. 7771
84.445
49
1.3028
64.066
1.3906
69-833
1. 490 1
75-403
1. 6012
80.768
1-7235
85-935
50
1.2657
65.065
1-3499
70.973
1.4456
76.671
1-5526
82.149
1.6706
87.417
Si
1.2287
66.049
1-3095
72.100
1-4015
77.929
1.5046
83.522
1.6184
88.890
52
1.1919
67.018
1.2693
73.217
1-3579
79.179
1-4572
84.890
1.5669
90356
53
I-I554
67.971
1.2295
74-324
I-3I47
80.422
1. 4104
86.252
1.5162
91.817
54
1.1191
68.909
1. 1900
75-421
1. 2719
81.659
1-3643
87.609
1.4664
93-275
55
1. 083 1
69-833
1-1509
76.508
1.2297
82.892
1.3188
88.963
I-4I74
94-731
56
1 -Q473
70.744
1.1121
77-589
1. 1879
84.122
1.2740
90.318
1-3693
96.188
57
1.0118
71.640
1-0737
78.663
1. 1467
85-350
1.2299
91.674
1.3221
97.646
58
0.97653
72.522
1-0358
79.730
1.1061
86.576
1. 1865
93.032
1.2758
99.108
59
0.94160
73-392
0.99826
80.795
1. 066 1
87.808
1 -1439
94.398
1-2305
100.577
60
0.90699
74.249
0.96117
81.859
1.0266
89.045
1. 1020
95-773
1.1861
102.057
61
0.87268
75-094
0.92451
82.919
0.98772
90.287
1 .0609
97-I58
1-1427
103.548
62
0.83871
75.926
0.88831
83.982
0.94946
91.540
1.0207
98.559
1. 1003
105.054
63
0.80508
76.748
0.85256
85.048
0.91182
92.807
0.981 19
99.978
1.0589
106.580
64
0.77177
77-56i
0.81727
86.121
0.87480
94.092
0.94254
101.420
1.0186
108.129
65
0.73879
78.365
0.78245
87.204
0.83842
95.400
0.90472
102.891
0.97928
109.707
66
0.70615
79.161
0.74810
88.300
0.80268
96.734
0.86773
104.394
0.94100
111.318
67
0.67383
79-951
0.71420
89.415
0.76759
98.101
0.86160
105.937
0.90378
112.968
68
0.64184
80.736
0.68078
90.551
o.733 J 4
99.508
0.79631
107.527
0.86764
114.663
69
0.61019
81.519
0.64782
91.717
0-69935
100.962
0.76190
109.170
0.83259
116.410
70
0.57887
82.300
0.61533
92.917
0.66624
102.473
0.72838
110.875
0.79865
118.215
7i
0.54786
83.084
0-58331
94.161
0.63379
104.050
0.69576
112.653
0.76583
120.087
72
0.51715
83.872
o-55i75
95-458
0.60202
105.706
0.66406
114.514
0.73414
122.035
73
0.48674
84.668
0.52065
96.819
0.5709S
107.453
0.63329
116.471
0.70361
1 24.068
74
0.45663
85477
0.49003
98-258
0.54061
109.308
0.60349
"8-537
0.67428
126.197
75
0.42680
86.304
0.45988
99-793
0.51 100
in. 291
0.57470
120.726
0.64618
128.432
76
0.39724
87.156
0.43021
101.445
0.48217
"3-423
0.54696
123.058
0.61934
130.785
77
0.36794
88.041
0.40104
103.241
0.4541S
"5-732
0.52030
125.550
0.59381
133.267
78
0.33888
88.972
0.37238
105-215
0.42701
118.248
0.49480
128.224
0.56965
135.890
79
0.31006
89.963
0.34428
107.409
0.40082
121.008
0-47055
131. 100
0.54691
138.664
80
0.28146
91.036
0.31679
109.880
0.37567
124055
0.44764
134.201
0.52568
141.601
81
0.25309
92.221
0.28997
112.701
0.35167
127.438
0.42617
137-553
0.50603
I44.7I3
82
0.22494
93-56i
0.26395
"5-971
0.32897
131. 210
0.40626
141. 172
0.48805
148.003
83
0.19700
95.128
0.23887
119.816
0.30779
135-433
0.38806
145.082
0.47184
I5J-474
84
0.16926
97-033
0.21497
124.413
0.28838
140.167
0.37174
149.292
0.45750
155-127
85
0.14177
99-473
0.19261
129.984
0.27102
I45-463
0.35749
153.806
0.44514
158.954
86
0.11467
102.829
0.17231
136.806
0.25603
I5I-356
o.3455o
158.614
0.43486
162.943
87
0.08809
107.920
0.15476
145.176
0.24378
I57-847
0-33593
163.691
0.42674
167.072
88
0.06261
116.850
0.14093
i55-3o6
0.23469
164.877
0.32895
168.991
0.42088
171-315
89
0.04025
136.057
0.13195
167. 116
0.22911
172.324
0.32472
174-453
o.4i734
I75-637
90
0.02920
180.000
0.12884
180.000
0.22720
180.000
0.32329
180.000
0.41615
180.000
Examples, cosh (2.0 /90 ) = 0.41615 /180 .
cosh -1 (0.54691 /i38.664) = 2.0 /79 .
["]
Table II. HYPERBOLIC COSINES, cosh (p [$) - r/f. Continued
2-3
2.4
2-5
45
2.0958
84-551
2.2636
89.050
2.4449
93.438
2.6403
97.730
2.8502
101.944
46
2.0350
86.159
2.1966
90.740
2.3711
95.202
2-5589
99.564
2.7603
103.842
47
1-9749
87-755
2.1306
92.417
2.2984
96.952
2.4788
101.380
2.6720
105.720
48
I-9I55
89.341
2.0655
94.081
2.2269
98.687
2.4001
103.179
2-5853
107.578
49
1.8569
90.917
2.0013
95-734
2.1567
100.408
2.3229
104.962
2.5004
109.417
5
1.7992
92.484
1.9382
97.376
2.0877
102. 116
2.2473
106.729
2.4I73
in. 238
Si
1.7424
94.043
1-8763
99.009
2.0200
103.812
2.1732
108.482
2.3361
1 13.041
52
1.6865
95-594
i-8i5S
100.633
1-9537
105.498
2.1008
110.220
2.2568
114.826
53
1. 6316
97.140
1-7559
102.249
1.8889
107.173
2.0301
1 1 1.944
2-1795
116.593
54
1-5777
98.681
1.6976
103.858
1.8255
108.838
1.9612
113.656
2.1042
118.344
55
1-5249
100.220
1.6406
105.462
1.7637
110.495
1.8940
"5-356
2.0310
120.079
56
1-4732
101.758
1.5848
107.063
1-7034
H2. 145
1.8286
117.045
1-9599
121.799
57
1.4226
103.296
1-5303
108.662
1.6447
II3.789
1-7651
118.724
1.8909
123.504
58
I-373I
104.836
1.4772
110.261
1.5876
U5-430
1-7035
120.394
1. 8241
125-195
59
1.3248
106.382
1.4256
1 1 1.862
1.5322
II7.069
1.6438
122.057
1-7594
126.874
60
1.2776
107.936
1-3754
113.467
1.4784
H8.708
1-5859
123-715
1.6969
128.541
61
1-2317
[ 09.501
1.3266
115.079
1.4262
120.347
1.5299
125.369
1.6366
130.198
62
1. 1870
[i 1.079
1.2792
116.700
I.3758
I2I.99I
I.4758
127.020
I-5785
131.846
63
1 -1435
112.673
1.2332
118.333
1.3270
I23.64I
1-4237
128.671
1.5226
I33.486
64
1.1012
[14.288
1. 1887
119.982
1.2799
I25.3OO
I.3736
130.322
1.4689
135-120
65
1.0602
115.928
I-I457
121.650
1-2345
I26.970
I.3254
131.977
I-4I73
136.749
66
1.0204
H7-597
1. 1042
123-339
1. 1908
I28.654
1. 2791
133-638
1-3679
138.374
67
0.98193
[ 19.299
1.0642
125055
1. 1488
130.355
1-2347
I35-306
1.3207
139.998
68
0.94474
[21.041
1.0256
126.801
1. 1086
132.077
1. 1923
136.985
1.2756
141.622
69
0.90886
[22.827
0.98860
128.581
1.0700
I33-823
1.1518
138.676
1.2327
143.247
70
0.87429
124.662
0.95308
130.400
1.0332
135-595
1.1132
140.382
1.1919
144-876
7i
0.84105
126.554
0.91908
132.263
0.99804
137-397
1.0765
142.106
1-1532
146.511
72
0.80915
128.509
0.88663
134-174
0.96464
139-233
1.0417
143.850
1.1166
148.153
73
0.77861 ]
[30.533
0.85573
136.137
0.93297
141. 106
1.0088
145.616
1.0821
149.803
74
0.74945 ]
[32.634
0.82638
138.158
0.90303
143.019
0.97785
147.407
1.0497
151.464
75
0.72171 ]
34.818
0.79862
140.242
0.87481
144.976
0.94877
149.225
1-0193
I53-I37
76
0.69541 ]
37-094
0.77246
142.393
0.84833
146.980
0.92156
151.071
099093
154.823
77
0.67060 1
39.468
0.74789
144.615
0.82360
I49-033
0.89622
152.948
0.96459
156.524
78
0.64732 ]
41.946
0.72497
146.911
0.80062
151-136
0.87276
I54.857
0.94026
158.241
79
0.62558 1
44-534
0.70372
149.285
0.77940
I53-29I
0.851 17
156.798
0.91793
159-974
80
0.60544 ]
47-237
0.68416
151-738
0.75996
155-499
0.83145
158.771
0.89757
161.723
81
0.58697 i
50.058
0.66632
154.271
0.74231
157.760
0.81361
160.778
0.87918
163.490
82
0.57021 ]
52-997
0.65024
156.883
0.72646
160.074
o.79764
162.817
0.86276
165.274
83
0.55523 1
56-054
0.63595
I59.572
0.71244
162.438
0.78354
164.888
0.84829
167.074
84
0.54209 ]
59-225
0.62349
162.334
0.70025
164.848
0.77131
166.987
0-83575
168.889
85
0.53085 ]
62.503
0.61287
165.164
0.68990
167.301
0.76095
169. 112
0.82518
170.717
86
0.52156 ]
65.876
0.60413
168.054
0.68141
169.793
o.75247
171.260
0.81650
172.558
87
0.51428 ]
69.329
o.5973i
170.994
0.67479
172.316
0.74587
I73.427
0.80979
174.409
88
0.50905 ]
72.849
0.59242
173-973
0.67006
174.863
0.74116
175.610
0.80499
176.269
89
0.50590 1
76.413
0.58948
176.980
0.66722
177.427
0.73834
177.803
0.80207
178.134
90 0.50485 180.000 0.58850 180.000 0.66628 180.000 0.73740 180.000 0.801 14 180.000
Examples, cosh (2.2 /45 ) = 2.2636 /89.o5o = 2.2636 /89.o3 , .oo'
cosh -1 (1.082 1 /i49.8o3) = 2.5 773.
[12]
Table II. HYPERBOLIC COSINES, cosh (p /a) = r [y. Continued
2.6
2.7
2.8
2.9
3-o
45
3-753
c 06.093
3-3163
1 10. 190
3-5741
114.248
3.8497
[18.275
4- 1443
122.282
46
2.9758
[ 08.05 1
3.2062
112.207
34523
116.322
3.7I46
[20.406
3-9945
124.469
47
2.8783
[ 09.987
3.0984
1 14. 199
33329
[ 18.368
3-5826
[22.506
3-8483
126.623
48
2.7827
[i 1. 901
2.9928
116.166
3.2162
120.387
34536
[24-575
3-7057
128.743
49
2.6891
H3-793
2.8896
1 18. 108
3.1023
[22.378
3-3278
[26.614
3-5667
[30.828
50
2-5977
115.663
2.7889
120.025
2.9913
[24.340
3-2053
[28.621
3-43 J 5
[32.879
Si
2.5085 :
ti7-5i2
2.6908
121. 917
2.8832
[26.273
3.0861
t30.595
35001
[34.894
52
2.4216
H9-340
2.5952
123.784
2.7780
[28.177
2.9703
[52-556
3.1726
[56.873
53
2.3369
t2i.i47
2.5023
125.626
2.6759
[30.052
2.8580
[34-444
3.0490
[38.815
54
2.2545 3
[22.931
2.4120
127.442
2.5769
[31.898
2.7492
[36.320
2.9294
[40.720
55
2.1745
[24.695
2.3245
129.233
2.4809
133-715
2.6439
[38.162
2.8137
[42.587
56
2.0970 ]
[26.440
2.2397
131.000
2.3880
[35-502
2.5421
[39.969
2.7020
[44415
57
2.0219 ]
[28.165
2-1577
132.742
2.2983
[37.259
2-4439
[41.742
2-5943
[46.203
58
1.9492 ]
29.872
2.0785
134.460
2.2118
[38.987
2.3492
[45-479
2.4905
[47-95 1
59
1.8790 ]
3i-5 6 o
2.0021
136.154
2.1284
[40.685
2.2580 ]
[45.180
2.3907
[49.659
60
1.8113 ]
133-231
1.9284
137.824
2.0481
[42.354
2.1703 ]
[46.846
2.2949
[5[-5 2 5
61
1.7460 ]
34.88s
1-8575
I39-47I
1.9709
[43-993
2.0861
[48.476
2.2030
[52.949
62
1.6832 ]
36.523
1.7894
141.095
1.8968 ]
[45.601
2.0053 ]
[50.071
2. 1 148
[54-55
63
1.6229 ]
38.146
1-7241
142.696
1.8259
[47.179
1.9280 ]
[51.627
2.0304
[56.067
64
1.5650 ]
39-754
1.6615
144.276
1.7580
[48.728
1.8541 ]
[53-346
1.9498
[57-559
65
1.5096 i
41-349
1.6016
145-834
1-6931
[50.247
I.783S 3
[54.628
1.8729
[59.005
66
1.4566 ]
42.932
1-5445
147-371
1.6311
[5I-737
1. 7162 ]
[56.071
1.7997
[60.406
67
1.4060 i
44.504
1.4900
148.887
1. 5721
[53-198
1.6522 ]
[57-477
1-7301
[61.759
68
1.3578 3
46.066
1.4382
150.384
1-5161
[54.628
I-59H 3
[58.844
1.6640
[63.064
69
I.3120 ]
47.620
1-3889
151-863
1.4629
[56.030
1-5338 ]
[60.172
1.6013
[64.321
70
I.2685 ]
49.164
1.3422
153-322
1.4126 1
57404
1-4793 3
61.460
1.5420
[65.528
7i
I.2273 3
5 -705
1. 2981
I54-764
1.3650 ]
58.749
1.4278 ]
62.709
1.4861
[66.685
72
1. 1885 1
5 2 -239
1-2565
156.189
1.3202 ]
60.066
1-3793 3
63.919
1-4355 3
[67.792
73
I.I5I9 3
53-77Q
1. 2174
157-599
1.2782 ]
6i.355
I-3338 3
65.090
1.3840 ]
[68.848
74
I.II76 I
55-298
1. 1807
158.994
1.2388 i
62.617
1. 2912 ]
66.222
1-3377 3
[69.853
75
1.0855 :
56.825
1. 1465
160.374
1.2020 ]
63-853
I-25H 3
67-315
1.2946 ]
70.806
76
1.0556 i
58.351
1.1147
161.742
1. 1677 ]
65.063
1. 2144 ]
68.370
1-2545 3
71.708
77
1.0278 ]
59.878
1.0852
163.096
1. 1360 ]
66.248
I. l8o2 ]
69.387
1. 2174 ]
[72.560
78
1.0022 ]
61.406
1.0580
164.440
1. 1069 ]
67.409
1. 1486 ]
70.368
1. 1832 ]
73.362
79
0.97880 ]
62.937
1-0331
165.773
1.0803 1
68.547
1. 1200 ]
7i-3!3
1.1519 ]
74.116
80
C95745 i
64.471
1-0105
167.096
1.0561 i
69.664
I.O938 ]
72.225
1.1235 >
74-823
81
0.93821 ]
66.008
0.99006
168.411
1.0342 1
70.760
I.0702 ]
73-104
1.0979 ]
75485
82
0.92106 ]
67-549
0.97189
169.718
1.0147 ]
71-837
I.O492 ]
73-953
1.0751 ]
76.104
83
0.90596 ]
69.094
0.95592
171.018
0.99765 3
72.897
1.0307 :
74-774
1.0550 l
76.685
84
0.89290 ]
70.643
0.942 1 1
172.312
0.98287 ]
73-942
1. 01 48 ]
75-571
1.0377 ]
77.229
85
0.88187 i
72.196
0.93045
173.601
0.97041 ]
74-973
1.0014 :
76.544
1.023 1 ]
77.742
86
0.87286 ]
73-752
0.92093
174.886
0.96025 ]
75-993
0.99042 ]
77.099
1.0112 ]
78.228
87
0.86587 ]
75-3"
o.9i354
176.168
o.95235 >
77.003
0.98190 ]
77.838
1.0019 :
78.691
88
0.86089 :
76.873
0.90827
177-447
0.94671 i
78.006
0.97582 ]
78.566
0.99528 ]
79-157
89
0.85789 ]
78.436
0.90512
178.724
o.94334 1
79.004
0.97217 ]
79-285
0.99130 ]
79-571
90
0.85689 i
[80.000
0.90407
180.000
0.94222 ]
80.000
0.97096 i
80.000
0.98999 ]
80.000
I
Examples
. cosh (2
8 /85 ) =
0.97041 ft
74-973 =
= 0.97041 /
'74-58'-
r
cosh -1 (1.5420 /i65.528) = 3.0 /70 .
[13]
Table III. HYPERBOLIC TANGENTS, tanh (p [$) = r [y
o.i
o-3
0.4
o-5
45
46
47
48
49
75
76
77
78
79
85
86
87
88
89
0.10000 44.812
0.10001 45.812
0.10002 46.812
0.10003 47.812
0.10004 48.813
50 0.10006 49.813
51 0.10007 50.813
52 0.10008 51.814
53 0.10009 52.816
54 0.10010 53.818
55 O.IOOII
56 0.10013
57 0.10014
58 0.10015
59 0.10016
60 0.10017
61 0.10018
62 0.10019
63 0.10020
64 0.10020
65 0.10021
66 0.10022
67 0.10023
68 0.10024
69 0.10025
70 0.10026
71 0.10026
72 0.10027
73 0.10028
74 0.10028
0.10029
0.10029
0.10030
0.10030
0.1003 1
80 0.1003 1
81 0.10032
82 0.10032
83 0.10032
84 0.10033
0.10033
0.10033
0.10033
0.10033
0.10033
54.820
55-823
56.825
57-828
58.830
59-833
60.837
61.841
62.845
63.849
64-853
65-857
66.862
67.866
68.871
69.877
70.882
71.888
72.893
73.898
74.904
75-9io
76.916
77.922
78.928
79-934
80.940
81.946
82.953
83.960
84.967
85-974
86.981
87.988
88.994
0.19997 44-235
0.20006 45.236
0.20015 46-237
0.20024 47- 2 39
0.20034 48.242
0.20043
0.20053
0.20062
0.20071
0.20081
49-245
50.251
51-256
52.262
53-268
0.20090 54.276
0.20099 55-285
0.20107 56.295
0.20115 57.306
0.20124 58.318
0.20132
0.20140
0.20148
0.20156
0.20164
0.20171
0.20179
0.20186
0.20193
0.20199
0.20206
0.20212
0.20217
0.20223
0.20228
0.20234
0.20239
0.20243
0.20246
0.20250
0.20254
0.20257
0.20260
0.20263
0.20265
0.20267
0.20268
0.20270
0.20270
0.20271
59-332
60.345
61.360
62.375
63-39I
64.408
65-425
66.443
67.461
68.480
69.501
70.522
71-544
72.566
73-589
74.612
75-635
76.659
77.684
78.709
79-734
80.759
81.785
82.812
83.838
84.864
85.891
86.918
87.946
88.973
0.29981 43.282
0.30012 44.281
0.30043 45.280
0.30075 46.283
0.30107 47.290
0.30138 48.297
0.30169 49-306
0.30201 50.315
0.30232 51.328
0.30263 52.344
0.30294
0.30325
0.3035S
0.30385
0.30414
53-362
54-382
55-404
56.426
57-452
0.30444 58.479
0.30473 59-5IO
0.30501 60.542
0.30528 61.575
0-30555 62.610
0.30580
0.30605
0.30630
0.30655
0.30678
0.30701
0.30722
0.30742
0.30762
0.30781
0.30799
0.30816
0.30831
0.30846
0.30860
0.30872
0.30884
0.30894
0.30904
0.30912
0.30920
0.30926
0.30930
0.30933
0.30934
63.647
64.686
65.727
66.769
67.813
68.859
69.906
7o.955
72.005
73-056
74.108
75.162
76.217
77-273
78.329
79.386
80.445
81.506
82.567
83.628
84.689
85.75I
86.813
87.875
88.937
0.39921 41-954
o.39995 42.945
0.40069 43.942
0.40143 44-942
0.40217 45-947
0.40293 46.955
0.40370 47.969
0.40446 48.986
0.40521 50.005
0.40596 51.031
0.40671 52.058
0.40746 53-089
0.40820 54.124
0.40892 55.164
0.40964 56.207
0.41037 57.255
0.41 107 58.305
0.41176 59.359
0.41244 60.417
0.41311 61.479
0.41376
0.4 1 44 1
0.41504
0.41565
0.41623
0.41680
0.4I735
0.41788
0.41838
0.41886
0.41932
0.41975
0.42016
0.42054
0.42088
0.42120
0.42150
0.42177
0.42201
0.42222
0.42239
0.42252
0.42264
0.42274
0.42279
62.544
63.612
64.685
65.760
66.837
67.918
69.002
70.089
71.179
72.272
73-368
74.466
75.566
76.668
77.771
78.876
79-983
81.092
82.203
83-3I5
84.427
85-540
86.654
87.768
0-49757 40.250
0.49902 41.229
0.50047 42.219
0.50192 43.213
0.50340 44-213
0.50490 45.220
0.50639 46.233
0.50789 47-252
0.50939 48.276
0.51089 49.308
0.51239
0.51389
0.51538
0.51687
0-51835
0.51983
0.52128
0.52271
0.52412
0.52552
0.52689
0.52824
0.52957
0.53085
0.53209
0.53330
o.53446
0.53560
0.53669
0-53773
0.53872
0.53965
0.54054
0.54138
0.54215
0.54285
o.54349
0.54407
o.54459
0.54503
0.54540
o.5457i
0.54596
0.54616
0.54628
50.344
51-388
52.439
53-494
54-556
55-625
56.700
57.78I
58.867
59-959
61.058
62.164
63.276
64.391
65-511
66.638
67.771
68.909
70.052
71.200
72.351
73.507
74.667
75.83I
76.999
78.170
79-344
80.520
81.699
82.881
84.065
85.251
86.438
87.626
88.813
90 0.10033 90.000 0.20271 90.000 0.30934 90.000 0.42280 90.000 0.54631 90.000
Note. tanh (o /8) =0 /y.
Examples, tanh (0.5 /6o ) = 0.51983 /55-625 = 0.51983 />m .X7'-3o'-
tanh" 1 (0.54628 /88.8i3) = 0.5 /8q.
[14]
Table III. HYPERBOLIC TANGENTS, tanh (p /5) - r [y. Continued
0.6
0.7
0.8
0.9
45
0.59406
38.183
0.68732
35-786
0-77577
33-098
0.85756
30.161
0.93077 27.044
46
0.59650
39.146
0.69109
36.719
0.78117
33.98o
0.86480
30.980
0.93909 27.784
47
0.59898
40.119
0.69495
37.663
0.78671
34.878
0.87229
3i-8i5
0.94950 28.539
48
0.60149
41.099
0.69888
38.617
0.79240
35-790
0.88001
32.666
0.95938 29.308
49
0.60403
42.088
0.70287
39-58i
0.79824
36-7I5
0.88799
33-531
0.96966 30.092
5
0.60660
43-085
0.70694
40.557
0.80421
37-653
0.89620
34.412
0.98032 30.892
5i
0.60920
44.092
0.71107
41-545
0.81031
38.605
0.90466
35-3io
-99!36 3!-7io
52
0.61182
45-107
0.71527
42.543
0.81655
39-573
0.91337
36.223
1.00282 32.545
53
0.61447
46.130
0.71952
43-555
0.82291
40.556
0.92231
37-155
1.01469 33.400
54
0.61713
47.162
0.72382
44-577
0.82940
41-554
0.93150
38.105
1.02697 34.274
55
0.61980
48.203
0.72817
45.612
0.83601
42.568
0.94094
39-075
103970 35.172
56
0.62248
49-254
0.73257
46.662
0.84274
43 599
0.95063
40.066
1.05287 36.091
57
0.62517
50.315
0.73700
47.725
0.84957
44.647
0.96056
41.078
1.06648 37.035
58
0.62785
51-384
0.74145
48.800
0.85649
45-712
0.97069
42. in
1.08054 38.004
59
0.63053
52.463
0.74593
49.888
0.86351
46.797
0.98106
43- J 67
1.09506 39.002
60
0.63322
53-552
0.75047
50.990
0.87063
47.900
0.99168
44.247
1.11009 40.026
61
0.63588
54-650
o.75499
52.107
0.87781
49.022
1.00251
45-353
1. 12555 41-082
62
0.63852
55-758
0.75950
53-238
0.88504
50.165
i-oi353
46.486
1.14144 42.168
63
0.641 15
56.876
0.76400
54-383
0.89232
5 J -327
1.02471
47.645
I-I5777 43-289
64
0.64376
58.002
0.76848
55-542
0.89965
52-509
1.03604
48.831
1. 17454 44-445
65
0.64633
59-I38
o.77294
56.716
0.90698
53-712
1-04753
50.044
1.19173 45638
66
0.64886
60.284
0.77737
57.902
0.91433
54-936
1. 059 1 6
51.289
1.20935 46.869
67
0-65135
61.439
0.78177
59-io5
0.92166
56.180
1.07090
52.562
1.22737 48.140
68
0.65380
62.603
0.78609
60.322
0.92894
57.448
1.08268
53.868
1.24569 49-455
69
0.65618
63-777
0.79033
6i-553
0.93616
58.737
1.09447
55-2Q4
1.26429 50.812
70
0.65850
64.959
0.79450
62.798
o.94332
60.047
1. 10627
56.572
1. 28316 52.215
7i
0.66075
66.150
0.79858
64.057
0.95037
6i.379
1.11803
57-974
1.30221 53.666
72
0.66294
67-35o
0.80256
65-329
0.95727
62.732
1. 12972
59.408
1.32140 55.164
73
0.66505
68.559
0.80641
66.614
0.96402
64.106
1.14126
60.874
1.34063 56.710
74
0.66708
69-775
0.81014
67-9I3
0.97060
65.501
1.15260
62.372
1.35986 58.307
75
0.66902
70.998
0.81371
69.225
0.97697
66.917
1. 16370
63.903
1.37894 59.957
76
0.67086
72.228
0.81713
70.550
0.983 1 1
68.352
i-i745o
65.468
1-39775 61.658
77
0.67261
73.466
0.82038
71.886
0.98898
69.808
1-18493
67.064
1. 41620 63.409
78
0.67425
74-7"
0.82345
73-233
0-99455
71.282
1 .19495
68.691
1.43412 65.212
79
0.67577
75.962
0.82632
74-591
0.99981
72-773
1.20447
7-347
1.45 141 67.065
80
0.67718
77.219
0.82899
75-958
1.00473
74.282
1. 21344
72.034
1.46790 68.968
81
0.67847
78.481
0.83144
77-334
1.00926
75-8o5
1. 22179
73-746
I.48345 70.919
82
0.67964
79-749
0.83366
78.719
1.01339
77-344
1.22946
75-483
1.49790 72.913
83
0.68068
81.021
0.83564
80.112
1.0x7x0
78.896
1.23640
77-243
1.51110 74.948
84
0.68159
82.296
0.83738
81.512
1.02036
80.460
1-24253
79.025
1.52289 77.023
85
0.68236
83-575
0.83887
82.917
1.02316
82.034
1. 24781
80.825
I-533I4 79-I32
86
0.68299
84.856
0.84009
84.328
1.02548
83.617
1. 25219
82.640
1. 54170 81.269
87
0.68349
86.140
0.84105
85-743
1.02730
85.206
1.25566
84.468
1.54848 83.429
88
0.68385
87.426
0.84173
87.161
1.02860
86.801
1. 25814
86.308
1-55339 85.609
89
0.68406
88.713
0.84214
88.580
1.02937
88.400
1-25963
88.153
1.55637 87.802
90
0.68413
90.000
0.84229
90.000
1.02960
90.000
1. 26015
90.000
1-55740 90-0 00
Eaxmples
tanh(o
9 /77) '
= 1. 1 8493 /67.o64
m 1.18493 /67.o.y
5o'.
tanlr 1
[0.66708 /6q.77S)
- 6 /74
[15]
Table III. HYPERBOLIC TANGENTS, tanh (p [8) - r /y. Continued
i-3
1.4
i-S
45 0.99389
23-833
I-0457
20.616
1.0857
17.464
1. "43
14.484
1-1323 1
ti.712
46
[.0049
24476
1.0582
21.144
1.0993
17.882
1. 1284
14-775
1. 1464 ]
1 1.884
47
[.0164
25-131
1.0713
21.685
1.1136
18.301
I-I433
15.064
1.1613 1
[2.048
48
[.0283
25-799
1. 085 1
22.236
1. 1286
18.721
1-1590
15-352
1. 1770 1
[2.208
49
t .0408
26.480
1.0995
22.798
1. 1445
19.148
I-I756
15.640
1. 1936
[2.362
SO
[0539
27.178
1.1147
23-371
1.1613
19.584
1. 1932
I5-930
1.2112
[2.510
Si
[.0676
27.891
1-1307
23-957
1. 1789
20.027
1.2118
16.222
1.2299
12.652
52
[.0818
28.621
1. 1474
24-558
1. 1976
20.479
1-2315
16.515
1.2498
[2.787
S3
[.0967
29.370
1. 1650
25-174
1. 2173
20.941
1.2524
16.811
1.2709
[2.914
54
[.1122
30.139
1-1835
25.807
1. 2381
21.414
1.2746
17. no
1-2933
13-035
55
[.1284
30.930
1.2030
26.460
1.2602
21.900
1.2982
I74I3
1.3172
[3-151
56
[-1453
31-744
1.2235
27-133
1.2836
22.401
1-3234
17.721
1-3427
[3.262
57
[.1629
32-583
1.2450
27.827
1.3084
22.918
1-3502
18.036
1.3700
[3.366
58
1.1813
33-449
1.2677
28.546
I.3346
23-452
I.3787
18.358
1.3992
[3.466
59
[.2005
34-343
1. 2916
29.292
1.3626
24.007
1.4093
18.689
14305
[3-559
60 i
[.2206
35-267
1.3168
30.068
1-3923
24.584
1. 442 1
19.032
1.4642
[3-651
61 ]
[2415
36.226
1-3434
30.876
1.4239
25.187
1.4772
19.389
1-5005
[3-738
62 ]
[.2632
37.222
I-37I4
31.720
1-4576
25.820
1.5148
19.761
I-5396
[3-824
63 I
[.2858
38-255
1.4009
32.603
1-4935
26.485
1-5553
20.150
1.5819
13.908
64 1
[.3094
39-328
1. 432 1
33-527
I-53I9
27.186
1-5990
20.562
1.6277
[3-99i
65 )
[-3339
40.446
1.4649
34.498
1.5729
27.928
1.6463
20.999
1.6776
[4.076
66 ]
[-3593
41.612
1-4995
35-520
1.6167
28.715
1.6974
21.465
I.73I9
14.166
67 1
[.3856
42.827
1-5359
36-597
1.6637
29-554
1.7528
21.966
I-79H
[4.261
68 i
[.4129
44.096
1-5743
37-737
1. 7140
30452
1.8131
22.507
1.8566
[4.364
69 1
[.4411
45.421
1.6148
38.941
1.7680
3I4I5
1.8788
23.096
1.9285
[4.480
70 i
[.4702
46.806
1-6573
40.219
1.8260
32452
1.9506
23.740
2.0078
14.612
71 ]
1.5001
48.256
1.7020
41-575
1.8882
33-57Q
2.0293
24.448
2.0959
[4-765
72 ]
[5307
49-773
1.7488
43-OI7
I-955I
34.782
2.1158
25.232
2.1942
[4.944
73 3
.5620
51-361
1.7977
44-553
2.0269
36.101
2.2111
26.106
2.3043
[5-159
74 3
t-5938
53.022
1.8488
46.190
2.1041
37-539
2.3164
27.084
2.4285
15419
75 J
.6261
54.762
1.9019
47-936
2.1869
39.110
24332
28.186
2.5694
15-734
76 ,
6585
56.581
1.9568
49.798
2.2757
40.830
2.5631
29433
2.7303
16.120
77 3
t.6910
58.482
2.0134
51-786
2.3706
42.720
2.7078
30.855
2.9157
[6.597
78 ]
.7232
60.468
2.0713
53-9o6
2.4716
44.798
2.8697
32.486
3-1312
17.186
79 J
i-755o
62.538
2.1299
56.165
2.5786
47.088
3-0509
34-367
3-3843
17.924
80 ]
1.7858
64.692
2.1887
58.571
2.6912
49.611
3-2536
36-546
3-6845
18.856
81
[-8155
66.931
2.2471
61.126
2.8085
52.39I
3.4807
39-085
4.0459
20.044
82 ]
1.8435
69.252
2.3040
63.832
2.9290
55447
3-7337
42.056
4.4876
21.578
83
[.8696
71.650
2-3585
66.690
3.0506
58.800
4-oi35
45-546
5-0365
23.588
84
1.8933
74.121
2.4094
69.694
3-I704
62.460
4-3i88
49.646
5-73"
26.276
85
[.9142
76.657
2-4555
72.836
3-2845
66.432
4.6429
54459
6.6297
29-955
86
[.9318
79.252
2-4955
76.102
3-3884
70.706
4.9729
60.069
7.8015
35-134
87
[.9460
81.895
2.5281
79-475
34767
75-253
5.2871
66.523
9-3413 -
12.644
88
[.9564
84.575
2.5523
82.933
3-5446
80.030
5-5531
73.786
11.259
53.726
89
[.9627
87.281
2.5671
86.452
3-5875
84.971
5-7333
81.707
13.182
59.695
9
[.9648,
90.000
2.5721
90.000
3.6021
90.000
5-9978
90.000
14.101 <
po.000
Examples.
tanh (1
4 764) =
1 -5990
/20.562
= 1.5990 /20.33'
43'-
tanh -1
[I-7550 /<
= i.i /79 e
[16]
Table III. HYPERBOLIC TANGENTS, tanh (p [$) = r [y. Continued
1.6
i-7
1.8
1.9
45
46
47
48
49
5
5i
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
7i
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
1.1413
1-1548
1.1691
1. 1842
1.2002
1.2171
1-2351
1-2541
1.2744
1.2960
1.3190
1-3435
1.3698
1-3979
1.4281
1.4606
1.4956
1-5334
1-5743
1.6187
1.6670
1. 7198
1.7777
1-8413
1.9116
1.9893
2.0759
2.1728
2.2819
2-4053
2.5461
2.7079
2.8957
3-H57
3.3766
3.6909
4.0755
4.5558
5.1722
5-9896
7.1203
8.7720
11.388
15.990
24.844
9.201
9.267
9.318
9-358
9-385
9.400
9.400
9-384
9-354
9-309
9.246
9.166
9.069
8-953
8.817
8.661
8.484
8.286
8.065
7.819
7.548
7.252
6.928
6-575
6. 191
5-776
5-326
4.840
4-3*4
3-744
3.127
2-457
1.726
0.922
0.034
0.960
2.087
3.390
4-937
6.839
9.289
12.668
17.791
26.760
46.011
,1428
1553
,1686
.1826
.1974
.2131
.2296
.2472
.2659
.2857
,3067
3292
3532
.3788
4063
4358
467S
5017
5386
5785
.6218
,6690
.7206
.7770
.9072
.9828
2.0667
2.1603
2.2652
2.3834
2.5172
2.6696
2.8442
3-0455
3.2790
3.S5I9
3-8718
4.2487
4.6927
5.2102
5-7994
6.4356
7-0503
7.5I93
6.984
6.952
6.902
6.834
6.749
6.645
6.520
6-373
6.203
6.008
5.788
5-539
5.261
4-953
4.611
4.232
3.819
3-365
2.869
2.326
1-734
1.090
0.387
0.376
1.209
2. 116
3.106
4.187
5-371
6.670
8.101
9.685
11.447
13-420
15.644
18.175
21.083
24.466
28.446
33*199
38.945
45-956
54-527
64.868
76.896
1385
5-063
1499
4-950
1618
4.814
1743
4.659
1876
4.480
.2016
.2163
.2318
.2483
.2657
.2842
3038
3247
.3469
.3706
3959
4230
.4521
4833
.5169
5531
5923
6347
.6807
73o8
.7854
.8451
.9105
9823
2.0613
2.1484
2.2446
2.35*0
2.4685
2.5984
2.7416
2.8987
3.0700
3-2540
3-4477
3-6459
3-8392
4-oi57
4-I592
4-2531
4-275
4-045
3-787
3-499
3-i8o
2.826
2.436
2.008
1.540
1.026
0.465
0.145
0.810
1-533
2.318
3-172
4.098
5.104
6.196
7.382
8.671
10.074
11.602
13.266
15.084
17.076
19.261
21.664
24.315
27.250
30.510
34.140
38.191
42.722
47-793
53.448
59.720
66.606
74-043
81.905
.1302
.1401
1505
.1614
.1728
1975
.2107
.2247
2394
2549
.2713
.2886
.3069
.3263
3470
.3689
3922
.4170
4435
.4718
.5022
5347
.5696
.6070
6474
.6908
7376
.7881
.8425
.9011
.9641
2.0317
2.1040
2.1809
2.2621
2.3469
2-4344
2.5230
2.6104
2.6940
2.7701
2.8350
2.8849
2.9163
3-438
3.260
3-058
2.832
2.578
2.295
1.981
1.634
1-253
0.835
o.379
0.121
0.666
1.259
1.905
2.606
3.366
4.191
5.085
6.052
7.099
8.232
9-459
10.786
12.221
13-773
15-454
17-273
19.244
21.379
23.692
26.202
28.925
31.881
35-088
38.568
42.344
46.428
50.842
55-590
60.673
66.075
71.768
77.700
83.805
1 191
1275
1363
1455
I550
1650
1754
1863
1977
2096
2939
.3106
.3281
.3466
.3662
.4086
4317
.4562
.4821
5095
.5385
5693
.6019
.6363
.6725
.7105
7503
.7917
.8344
.8781
.9222
.9661
2.0090
2.0497
2.0872
2.1202
2.1476
2.1680
2.1807
2.094
1.867
1.613
1-333
1.023
0.681
0.306
0.103
0.550
1.039
2220 1.571
2350 2.149
2487 2.777
2630 3.458
2781 4.195
4995
5.860
6-793
7.802
8.891
10.068
".338
12.707
14.184
I5.776
17.490
19-337
21.326
23.466
25.769
28.245
30.905
33760
36.820
40.093
43-59
47-319
51.281
55-474
59.894
64.528
69-359
74-359
79.494
84.723
90 34.232 90.000 7.6968 90.000 4.2863 90.000 2.9271 90.000 2.1850 90.000
Note. Negative quantities are in heavy type.
Examples, tanh (1.6/54) = 1.2060 /q-3Q9 = i.2q6q /qaS'.^"-
tanh (2.0 /64 ) = 1.3662 \8.8 9 i = 1.3662 \8.53'.28'.
tanh" 1 (1.4718^099) = 1 -9 /65-
[17]
Table III. HYPERBOLIC TANGENTS, tanh (p /J) =r /y. Continued
2-3
2.4
2-5
45
1. 1065
1.007
1.0932
o.i55
[.0799
0.492
1.0672
0.961
I-0553
I.283
46
1.1134
0.746
1.0987
0.127
[.0842
0.783
1.0702
1.252
1-0573
I.564
47
1 . 1 206
0.458
1. 1044
0.436
[.0884
I.IOI
I.0732
1567
I.O592
1.868
48
1. 1280
0.141
1.1102
0.774
[.0927
1.446
1.0762
1.908
I.061O
2.195
49
I-I357
0.206
1.1161
1. 142
t.0970
1.820
1.0790
2.277
I.0626
2.548
5
I-I437
0.586
1. 1222
1.542
[.1013
2.226
1.0818
2.676
1 .0640
2.929
5i
1.1519
I.OOI
1. 1284
1.978
[.1056
2.666
1.0845
3-107
1-0653
3-340
52
1. 1604
1.452
I-I347
2.452
[.1099
3-144
1.0870
3-572
I.0663
3.782
53
1-1693
1-943
1.1411
2.965
[.1142
3-659
1.0894
4-073
I.067I
4256
54
1. 1784
2.476
1. 1477
3.520
[.1185
4.215
1.0917
4.614
I.0676
4.766
55
1. 1878
3-055
I-I544
4.120 ]
[.1227
4.815
1 -093 7
5.196
I.0678
5-314
56
1. 1976
3.682
1.1612
4.769 ]
.1268
5-462
I-0955
5.822
I.0677
5-903
57
1.2078
4.361
1.1681
5.469 ]
.1309
6.160
1.0971
6.496
I.0672
6-534
58
1. 2183
5-094
1-1751
6.226 i
.1348
6.912
1.0984
7.220
I.0662
7.211
59
1.2292
5.888
1. 1822
7.042 ]
.1386
7.722
1.0993
7.998
I.0647
7.938
60
1.2405
6-745
1. 1894
7.921 ]
.1422
8.594
1.0999
8.835
I.0628
8.718
61
1.2522
7.671
1. 1967
8.869 ]
1457
9-531
I.IOOI
9-735
I.0603
9-556
62
1.2644
8.669
1. 2041
9.889 i
.1490
10.540
1.0999
10.701
I.O572
10.455
63
1. 2771
9-744
1.2116
10.988 i
.1520
11.625
1.0992
11.740
1-0535
11.419
64
1.2903
10.902
1. 2192
12. 171 ]
.1548
12.791
1.0980
12.855
I .O49O
12.455
65
i-339
12. 151
1.2268
13-443 1
1573
14.044
1.0962
14-053
I.O438
13567
66
1.3181
13496
1.2344
14.810 ]
1595
15390
1.0939
15-341
I.O378
14.761
67
I-3329
14.942
1. 2421
16.280 ]
.1613
16.836
1 .0909
16.723
1. 03 IO
16.044
68
1-3483
16.499
1.2499
17-858 ]
.1628
18.389
1.0872
18.208
I.O232
17.424
69
1.3642
18.172
1.2576
19-552 ]
.1639
20.056
1.0829
19.802
I. OI45
18.906
70
1.3808
19.968
1.2654
21.370 ]
.1645
21.843
1.0779
21.514
I.OO49
20.500
7i
1.3980
21.898
1.2732
23-3I9 1
.1647
23-759
1.0721
23-352
O.99427
22.215
72
I-4I59
23.968
1.2809
25.405 ]
.1644
25.811
1-0655
25-324
O.98265
24.061
73
1-4344
26.185
1.2885
27.636 ]
.1637
28.006
1.0582
27-439
O.97006
26.048
74
1-4535
28.560
1. 2961
30.020 j
.1625
30.352
1.0501
29.706
O.95649
28.187
75
1-4732
31.099
1.3036
32.564 ]
.1608
32.858
1-0413
32.134
O.94202
30.489
76
J-4934
33-8n
1. 3109
35-274 3
1587
35-531
1.0318
34-730
O.9267I
32.966
77
I-5HO
36.702
1.3181
38.156 ]
.1561
38.374
1.0218
37-505
O.9I068
35633
78
1-5348
39-778
1 -3 2 5i
41.212 ]
I53 1
41.392
1.0113
40.467
O.89405
38.501
79
1-5559
43-043
i.33i8
44.446 :
.1498
44.590
1 .0004
43.620
O.8770I
41.582
80
1.5768
46-501
L3383
47-859 3
.1462
47.968
0.98931
46.968
O.85979
44.887
81
1-5974
50.151
1-3444
51.449 ]
1425
5L527
0.97822
50.517
O.84264
48.427
82
1.6174
53989
1.3500
55-212 a
1387
55264
0.96733
54267
O.82584
52.209
83
1.6364
58.011
I -3552
59-140 3
1349
59-171
0.95686
58.212
O.80977
56233
84
1.6541
62.210
J -3599
63.223 ]
.1312
63237
0.94710
62.344
0.79476
60.499
85
1.6700
66.570
1.3640
67.449 1
.1279
67.450
0.93826
66.650
O.7812O
64.994
86
1.6837
71.070
L3674
71.800 1
.1250
71-793
0.93061
71. 113
O.76946
69.703
87
1.6949
75.690
1.3702
76.254 3
.1225
76.245
0.92439
75-7IO
O.7599I
74.598
88
1. 7031
80.406
1.3722
80.79O I
.1207
80.781
0.91979
80.413
0.75283
79.645
89
1. 7081
85.187
J -3734
85.38I J
.1196
85.376
0.91696
85.188
0.74849
84.796
90
1.7099
90.000
J -3738
90.000 1
.1192
90.000
0.91601
90.000
O.74702
90.000
Note.
Negative quantit
ies are in heavy type.
Examples
. tanh (2.1 /48 ) =
1. 1 280 /o.i4i
= 1. 1280
/o.o8'.28'
t
tanh (2.1 /49 ) =
I-I357 \o.2o6
= I.I357
\o 6 I2'.22'
>
tanh -
1 (1-0318 \34-73o)
= 2.4/76.
[18]
Table III. HYPERBOLIC TANGENTS, tanh (p [S) = r [y. Continued
2.6
2.7
2.8
2.9
3-
45
1.0445
1.480
1.0348
1-576
1.0264
1-595
I.0192
1-554
1.0131
I.468
46
1.0456
1.744
1-0352
1.821
1.0262
1.816
1.0185
1.748
I.OI20
1-637
47
1.0465
2.030
1-0354
2.083
1.0257
2.051
1.0175
1-955
I.OIO7
I.8I5
48
1 -0473
2337
I-0353
2.365
1.0250
2.303
1.0163
2.175
I. OO9 1
2.002
49
1.0479
2.667
1-0350
2.666
1.0240
2.572
1. 0148
2.409
I.OO72
2.I98
50
1.0483
3.022
1.0344
2.988
1.0227
2.857
1. 01 29
2.656
I.OO49
2.405
5i
1.0483
3-403
1-0335
3-332
1.0210
3- 1 60
1. 0106
2.916
I.OO23
2.622
52
1 .0480
3.812
1.0323
3.700
1. 0189
3.483
1.0080
3-I9I
O.99922
2.849
53
1 -Q475
4250
1.0307
4.094
1.0164
3.826
1.0049
3.481
O.99572
3.086
54
1.0466
4-717
1.0286
4-513
i.oi35
4.190
1.0013
3.788
O.99174
3-334
55
1.0452
5.219
1.0260
4-959
I.OIOI
4-577
0.99722
4.112
O.98722
3-593
56
1.0434
5-756
1.0230
5-437
1. 006 1
4.987
0.99254
4-452
O.982II
3.862
57
1.0412
6.331
1.0194
5-945
1.0015
5-422
0.98724
4.810
O.97637
4.141
58
1.0385
6.947
1.0152
6.487
0.99625
5-884
0.98126
5-186
0.96995
4-432
59
1-0351
7.606
1. 0104
7.066
0.99027
6-374
0-97454
5-582
O.96279
4-735
60
1.0311
8.313
1 .0048
7.684
0.98353
6.895
0.96701
5-999
O.95481
5-049
61
1.0265
9.069
0.99847
8.343
0.97597
7-449
0.95862
6-439
0-94597
5-375
62
1.0211
9.879
0.99129
9.048
0.96751
8.036
0.94930
6.904
O.93619
5-7U
63
1.0149
10.747
0.98322
9.801
0.95807
8.660
0.93897
7-392
O.9254O
6.063
64
1.0079
11.677
0.97420
10.607
0.94760
9.325
0.92756
7.907
O.9I352
6.426
65
0.99990
12.675
0.96414
11.470
0.93603
10.033
0.91500
8.452
O.9OO47
6.801
66
0.99099
13747
0.95300
12.393
0.92328
10.789
0.90121
9.027
O.88618
7.192
67
0.98106
14.898
0.94070
13383
0.90927
11.599
0.88612
9-639
O.87055
7-598
68
0.97006
16.136
0.92720
14.449
0.89396
12.464
0.86964
10.289
0.85350
8.021
69
0-95794
17.469
0.91243
15-597
0.87726
13.396
0.85169
10.982
O.83495
8.463
70
0.94467
18.902
0.89635
16.833
0.85912
14-399
0.83221
11.722
O.81482
8.926
7i
0.93022
20.451
0.87893
18.168
0.83950
15-482
0.81113
12.518
0.79302
9.414
72
0.91458
22.122
0.86013
19613
0.81834
16.655
0.78839
13-378
O.76946
9-932
73
0.89775
23.929
0.83994
21.184
0.79562
17-931
0.76394
14-310
O.74408
10.485
74
0.87976
25.884
0.81839
22.893
0.77134
19325
0.73774
I5-328
O.71683
11. 081
75
0.86066
28.003
0.79552
24-757
0.74551
20.857
0.70977
16.448
O.68765
11.729
76
0.84053
30.302
0.77140
26.799
0.71815
22.547
0.68005
17.690
O.6565O
12.443
77
0.81949
32.799
0.74612
29.038
0.68938
24.421
0.64861
19.078
O.62338
13241
78
0.79769
35-513
0.71985
3I-505
0.65930
26.512
0.61551
20.647
O.58829
14.146
79
o.77535
38.466
0.69278
34-231
0.62807
28.861
0.58087
22.437
0.55I29
15.191
80
0.75271
41.678
0.66520
37-249
0.59596
31.519
0.54486
24.504
0.51245
16.419
81
0.73010
45-171
0.63743
40-599
0.56326
34-543
0.50773
26.921
O.4719O
I7-893
82
0.70790
48.966
0.60990
44-322
0.53039
38.004
0.46981
29.784
O.42986
19.700
83
0.68652
53-078
0.583 n
48.464
0.49791
41.989
0.43156
33-221
O.38661
21.976
84
0.66645
57-517
0.55765
53-o6o
0.46648
46.591
0.39363
37.403
0.34257
24.916
85
0.64820
62.286
0.53421
58.143
0.43691
5I-907
0.35689
42.549
O.29833
28.839
86
0.63230
67.370
o.5i353
63.722
0.41024
58.025
0.32255
48.931
O.2549I
34-254
87
0.61928
72.740
0.49636
69.778
0.38762
64.988
0.29220
56.833
0.21393
41.990
88
0.60959
78.349
0.48347
76.253
0.37028
72.762
0.26791
66.456
O.I78I5
53-294
89
0.60361
84.129
o.47544
83.042
0.35929
81.195
0.25198
77.709
O.I5225
69.480
90
0.60160
90.000
0.47273
90.000
0.35553
90.000
0.24641
90.000
O.I4255
90.OOO
Note. Negative quantites are in heavy type.
Examples tanh (2.6 /65 ) = 0.99990 /i2,675 = 0.99990 /i2.4.o'.$o*
tanh" 1 (0.88618 \7.i 9 2) = 3-0 /66.
[19]
Table IV. CORRECTING FACTOR.
sinh 6
e
r [7
o-3
0.4
o-5
45
1. 00000
0.096
1. 00000
0.383
1. 00000
0.860
1. 000 1 3
1-532
1.00032
2.391
46
0.99993
0.095
0-99975
0.382
0.99950
0.858
0.99920
1-529
0.99888
2.388
47
0.99987
0.095
0.99950
0.381
0.99897
0.856
0.99828
1.526
0.99744
2.385
48
0.99981
0.094
0.99930
0.380
0.99847
0.854
0-99733
1.520
0.99598
2.378
49
0-99975
0.094
0.99910
0.378
0.99797
0.852
0.99640
I.5I3
0.99454
2.368
50
0.99970
0.094
0.99880
0.376
0.99743
0.848
o-9955o
1.506
0.99312
2-357
Si
0.99965
0.093
0.99860
o.374
0.99690
0.842
0.99460
1.497
0.99170
2.342
52
0.99960
0.092
0.99840
0.371
0.99640
0.834
0.99370
1.486
0.99028
2-325
53
0-99955
0.091
0.99815
0.367
0.99590
0.826
0.99280
1.472
0.98888
2.304
54
0.99950
0.090
0-99795
0.362
0.99540
0.818
0.99190
1.458
0.98748
2.281
55
0.99944
0.089
o.99775
o-357
0.99490
0.809
0.99103
1.440
0.98610
2.254
56
0.99939
0.088
0-99755
0.352
0.99443
0.799
0.99018
1.421
0.98476
2.226
57
o.99933
0.086
o.9973o
0-347
o.99397
0.787
0.98930
1.400
0.98344
2.195
58
0.99928
0.085
0.99705
0.342
0-99347
o.773
0.98845
1-378
0.98212
2.160
59
0.99922
0.083
0.99685
0.336
0.99300
0.760
0.98763
1-354
0.98082
2.123
60
0.99917
0.082
0.99670
o.33i
0.99257
0.746
0.98685
I-330
0.97956
2.085
61
0.99912
0.081
0.99645
0.324
0.99213
0.731
0.98603
1.302
0.97832
2.042
62
0.99907
0.079
0.99625
0.317
0.99170
0.715
0.98523
1-273
0.97710
1.998
63
0.99902
0.077
0.99605
0.309
0.99127
0.698
0.98448
1.243
0.97590
1.950
64
0.99897
0.075
o.99585
0.301
0.99083
0.680
0-98373
1. 212
0.97476
1.900
65
0.99893
0.073
0.99570
0.293
0.99040
0.661
0.98300
1. 179
0.97364
1.848
66
0.99889
0.071
0-99555
0.284
0.99000
0.641
0.98232
1. 144
0.97254
1.794
67
0.99885
0.069
0.99540
0.275
0.98963
0.621
0.98165
1. 108
0.97150
1.738
68
0.99881
0.066
0.99520
0.265
0.98927
o-599
0.98100
1.070
0.97046
1.679
69
0.99877
0.064
0.99505
o-255
0.98891
0-577
0.98035
1.030
0.96946
1.617
70
0.99873
0.062
0.99490
0.245
0.98857
o.555
0-97975
0.990
0.96852
1-554
7i
0.99869
0.059
o.99475
0-235
0.98823
0.532
0.97918
0.948
0.96760
1.489
72
0.99865
0.057
0.99460
0.225
0.98790
0.508
0.97863
0.905
0.96676
1.422
73
0.99861
0.054
o.99445
0.214
0.98760
0.483
0.97808
0.861
0.96592
1-354
74
0.99858
0.051
0-99435
0.203
0.98733
0.458
0.97758
0.817
0.96514
1.284
75
0.99855
0.048
0.99425
0.192
0.98707
0.432
0.97710
0.771
0.96440
1. 212
76
0.99852
0.045
0.99415
0.180
0.98680
0.406
0.97665
0.724
0.96368
1. 138
77
0.99850
0.042
0.99405
0.168
0.98653
0-379
0.97625
0.676
0.96304
1.062
78
0.99847
0.039
0-99395
0.156
0.98633
0.351
0.97585
0.628
0.96246
0.986
79
0.99845
0.036
0.99385
0.144
0.98613
0.322
0-97545
o.578
0.96190
0.909
80
0.99843
0.033
0-9937S
0.131
0.98593
0.294
0.97512
0.528
0.96134
0.830
81
0.99841
0.030
0.99365
0.118
0.98577
0.266
0.97483
o.477
0.96088
0.750
82
0.99839
0.026
0.99360
0.106
0.98563
0.238
0.97458
0.425
0.96046
0.669
83
0.99838
0.023
0-99355
0.093
o.98553
0.209
0.97433
o.373
0.96008
0.587
84
0.99837
0.020
0-99350
0.080
0.98543
0.180
o.974i3
0.321
o.95974
0-505
85
0.99836
0.017
0-9934S
0.067
0.98537
0.150
o.97395
0.268
o.95944
0.422
86
0-99835
0.014
0.99340
0.054
0.98530
0.120
0.97380
0.215
0.95920
o-338
87
0.99834
O.OII
0-99335
0.041
0.98523
0.090
0.97370
0.162
0.95904
0.254
88
0.99833
0.008
0-99335
0.028
0.98517
0.060
0.97365
0.108
0.95894
0.170
89
0.99832
0.004
0-99335
0.014
0.98510
0.030
0.97360
0.054
0.95890
0.085
90
0.99831
0.000
0-9933S
0.000
0.98507
0.000
0-97355
0.000
0.95886
0.000
Note.
sinh 9
e
1.0 when 6 = o/g.
sinh (0.3 /69 ) _ _ .
Example. *T^ = 0.98891 /o.577 = 0.98891 /o-34 -37
0-3/62!
[20]
Table IV. CORRECTING FACTOR.
sinh 6
6
m r /y. Continued
0.6
0.7
0.8
0.9
45
1.00070
3-44Q
1.00134
4.676
1.00230
6.108
1.00363
7.728
1-00553
9-531
46
0.99863
3-437
0.99849
4.679
0.99856
6. 112
0.99893
7-735
0-99975
9546
47
0.99655
3-434
0.99564
4.676
0.99484
6.109
0.99425
7-734
0.99394
9-550
48
0.99445
3 426
0.99281
4666
0.991 14
6.099
0-98955
7-725
0.98816
9-543
49
0.99237
3-414
0.98999
4.652
0.98745
6.082
0.98488
7.707
0.98242
9-525
5
0.99030
3-398
0.98717
4.632
0.98379
6.058
0.98026
7.679
0.97672
9-495
5i
0.98825
3-379
0.98439
4.606
0.98015
6.026
0-97567
7.642
0.97105
9-453
52
0.98623
3-355
0.98161
4-574
0.97655
5-987
0.971 1 1
7-595
0.96543
9-399
53
0.98421
3-326
0.97887
4-537
0.97298
5 -94o
0.96659
7-538
0.95986
9333
54
0.98220
3-293
0.97616
4-493
0.96944
5.886
0.962 1 1
7.472
o.95435
9-255
55
0.98023
3-256
o.97349
4-445
0.96594
5.824
0.95769
7-396
0.94890
9.166
56
0.97830
3-215
0.97084
4-391
0.96249
5-755
0-95333
7.312
0-94353
9.065
57
0.97638
3-i7i
0.96823
4-331
0.95909
5.678
0.94904
7.218
0.93825
8.952
58
0.97448
3.122
0.96564
4-265
0-95574
5-593
0.94482
7.114
0.93305
8.827
59
0.97262
3.069
0.96313
4-193
0.95244
5-502
0.94067
7.000
0.92795
8.691
60
0.97081
3-oi3
0.96067
4.117
0.94923
5-405
0.93661
6.878
0.92295
8-544
61
0.96903
2-953
0.95826
4.036
0.94608
5-3oo
0.93263
6.747
0.91805
8.385
62
0.96728
2.889
0.95589
3-951
0.94299
5.189
0.92874
6.607
0.91325
8.215
63
0.96557
2.821
o-95356
3-859
0.93996
5.070
0.92493
6.458
0.90856
8.033
64
0.96390
2.749
0.95130
3.762
0.93703
4-944
0.92121
6.300
0.90400
7.841
65
0.96228
2.674
0.9491 1
3.661
0.93416
4.812
0.91761
6.136
0.89957
7.637
66
0.96072
2.596
0.94697
3-554
0.93140
4.674
0.91411
5.962
0.89527
7.424
67
0.95922
2-515
0.94493
3-444
0.92873
4-529
0.91074
5.780
0.891 1 1
7.201
68
o.95775
2.430
0.94293
3-329
0.92614
4-379
0.90747
5-590
0.88708
6.968
69
0.95632
2.342
0.94100
3.209
0.92364
4.223
0.90430
5-392
0.88320
6.723
70
o.95495
2.251
0.93914
3-085
0.92123
4.061
0.90127
5-i87
0.87947
6.469
7i
0.95365
2-157
O.03737
2-957
0.91891
3-894
0.89837
4-975
0.87589
6.207
72
0.95242
2.06 1
0.93569
2.825
0.91671
3.722
0.89558
4-756
0.87247
5.936
73
0.95123
1.962
0.93407
2.689
0.91461
3-544
0.89292
4-530
0.86921
5-656
74
0.95010
1.860
0.93254
2-550
0.91261
3-36i
0.89041
4.298
0.86612
5-368
75
0.94902
1-756
0.93109
2.408
0.91073
3-J74
0.88804
4-059
0.86320
5.072
76
0.94802
1.649
0.92973
2.263
0.90895
2.982
0.88581
3-8i5
0.86045
4.769
77
0.94707
1.540
0.92846
2. 114
0.90729
2.787
0.88372
3-566
0.85788
4-458
78
0.94620
1.429
0.92727
1.962
0.90574
2.588
0.88177
3-312
0.85549
4-I4I
79
0.94540
i-3i7
0.92617
1.808
0.90431
2-385
0.87997
3-053
0.85328
3-8i8
80
0.94465
1.203
0.92516
1.652
0.90301
2.179
0.87831
2.789
0.85125
3-489
81
o.94397
1.087
0.92424
1-493
0.90183
1.969
0.87681
2.522
0.84940
3-156
82
0.94337
0.970
0.92343
1-332
0.90076
1-757
0.87547
2.251
0.84774
2.817
83
0.94283
0.852
0.92270
1. 169
0.89981
1-543
0.87428
1.976
0.84628
2-474
84
0.94237
0.732
0.92207
1.005
0.89899
1.327
0.87324
1.699
0.84501
2.128
85
0.94197
0.612
0.92153
0.839
0.89829
1. 109
0.87237
1.420
0.84393
1.779
86
0.94163
0.490
0.92109
0.673
0.89771
0.889
0.87164
1.138
0.84305
1.426
87
0.94138
0.368
0.92074
0.506
0.89726
0.668
0.87108
0.855
0.84236
1.07 1
88
0.94122
0.246
0.92050
0.338
0.89694
0.446
0.87068
0.571
0.84186
0.715
89
0.941 10
0.123
0.92036
0.169
0.89675
0.223
0.87043
0.286
0.84156
0.358
90
0.94107
0.000
0.92031
0.000
0.89670
0.000
0.87037
0.000
0.84147
0.000
Example.
sinh (1.0
785)
: 0.84393 /
'i-779 :
= O.84303 /i.46'.
44'.
i.o 785
[21]
Table IV. CORRECTING FACTOR.
sinh 8
e
= 7 Ay. Continued
i-3
1.4
i-5
45
1.0081
11. 519
1.0115
13.692
1.0158
16.034
1.0212
18.568
1.0279
21.262
46
I.OOII
"543
1. 003 1
13.726
1.0060
16.092
1.0099
[8.639
1.0148
21-355
47
0.99409
n-555
0.99475
13-748
0.99623
16.128
0.99850
[8.689
1. 0018
21.426
48
0.98709
n-553
0.98650
13-753
0.98654
16.142
0.98729
[8.717
0.98893
21.474
49
0.98018
"536
0.97825
13-741
0.97685
16.137
0.97607
[8.723
0.97613
21.496
5
0.97327
11.506
0.97008
13.712
0.96722
16.113
0.96493
[8.707
0.96340
21.492
5i
0.96636
1 1. 461
0.96192
13.666
o.9577o
16.068
0-95393
[8.668
0.95080
21.462
52
0.95964
1 1. 401
o-95383
13.603
0.94822
16.004
0.94300
[8.605
0.93833
21.405
S3
0.95291
11.327
0.94583
I3-523
0.93892
15919
0.93221
[8.519
0.92593
21.321
54
0.94627
11.239
0.93800
I3-425
0.92969
15.814
0.92157
[8.409
o.9i373
21.210
55
o-93963
11. 136
0.93017
i3-3io
0.92054
15.688
0.91100
[8.275
0.90167
21.072
56
0.93318
11.019
0.92250
13.178
0.9 1 1 54
15-542
0.90064
[8.117
0.88980
20.907
57
0.92682
10.888
0.91492
13.028
0.90269
I5.376
0.89043 I
[7.936
0.87813
20.713
58
0.92054
10.742
0.90750
12.860
0.89400
15.188
0.88036 I
17-730
0.86667
20.491
59
0.91436
10.581
0.90017
12.675
0.88546
14.980
0.87050
[7.500
0.85540
20.240
60
0.90836
10.406
0.89300
12.474
0.87715
14-752
0.86086 ]
17.246
0.84433
19.964
61
0.90244
10.218
0.88600
12.255
0.86892
14.502
0.85136 !
[6.967
0-83353
19-657
62
0.89666
10.016
0.87918
12.019
0.86092
14.232
0.84214 ]
[6.663
0.82300
19.321
63
0.89103
9.800
0.87250
11.767
0.85315
13-942
0.83314 ]
6-335
0.81273
18.956
64
0.88554
9-57Q
0.86600
11.497
0.84554
13.632
0.82436 ]
[5-983
0.80267
18.562
65
0.88019
9-327
0.85967
11. 211
0.83808
13-301
0.81579 ]
[5.607
0.79293
18.140
66
0.87501
9.071
0.85350
10.909
0.83094
12.950
0.80750 ]
5.207
0.78347
17.690
67
0.86998
8.801
0.84758
10.594
0.82400
12.580
0.79950 ]
[4-783
C77433
17. 211
68
0.86514
8.519
0.84183
10.257
0.81731
12. 191
0.79171 ]
[4-335
0.86547
16.704
69
0.86045
8.225
0.83625
9.907
0.81077
11.783
0.78421 ]
[3-865
0-75693
16.169
70
0.85596
7.918
0.83093
9-543
0.80454
n-357
0.77707 1
[3-373
0.74873
15.607
7i
0.85165
7.600
0.82583
9.164
0.79862
10.912
0.77021 ]
2.858
0.74087
15.018
72
0.84754
7.271
0.82095
8.771
0.79292
10.450
0.76364 1
2.322
0-73333
14.402
73
0.84362
6.931
0.81631
8-365
0.78746
9.971
0.75736 3
[1-765
0.72620
13.761
74
0.83989
6.580
0.81 190
7.946
0.78231
9.476
0.75I43 ]
[i. 188
0.71940
13.096
75
0.83637
6.220
0.80773
7-514
0.77746
8.966
0-74579 1
[0.591
0.71293
12.406
76
0.83306
5-850
0.80380
7.069
0.77287
8.440
0.74050
9-975
0.70687
11.693
77
0.82996
5-471
0.80013
6.614
0.76858
7.900
0-73557
9-342
0.70120
10.958
78
0.82707
5.084
0.79671
6.148
0.76459
7-346
0.73093
8.692
0.69593
10.201
79
0.82441
4.689
0-7935S
5.672
0.76090
6.780
0.72664
8.026
0.69107
9-425
80
0.82196
4.286
0.79065
5-i8 7
0-7S75I
6.202
0.72279
7-346
0.68660
8.630
81
0.81975
3-877
0.78802
4-693
o.75444
5-6i4
0.71921
6.651
0.68253
7.818
82
0.81775
3.462
0.78566
4-i9i
0.75165
5.016
0.71600
5-944
0.67887
6.991
83
0.81599
3.041
0.78358
3-68 3
0.74923
4.408
0.71319
5-227
0.67567
6.149
84
0.81445
2.616
0.78175
3.169
0.7471 1
3-793
0.71073
4.499
0.67287
5.294
85
0.81315
2.186
0.78022
2.649
o.7453i
3-i7i
0.70864
3.762
0.67047
4.429
86
0.81209
1-753
0.77895
2.124
0.74383
2-544
0.70694
3018
0.66847
3-554
87
0.81125
I-3I7
0-77797
1.596
0.74268
1.912
0.70561
2.269
0.66693
2.673
88
0.81066
0.879
0.77727
1.065
0.74185
1.277
0.70466
I-5IS
0.66587
1-785
89
0.81031
0.440
0.77684
0-533
0.74136
0.639
0.70409
0.758
0.66521
0.893
90
0.81019
0.000
0.77670
0.000
0.74120
0.000
0.70389
0.000
0.66499
0.000
Example.
sinh (1.5 /65 )
i-sZ6s!
= 0.79293 /i8.i4Q = 0.79293 /i8.o8'.24*.
[22]
Table IV. CORRECTING FACTOR.
sinh 6
d
/y. Continued
1.6
i-7
1.8
i. 9
45
i-359
24.117
1.0456
27-133
1.0572
30.292
1.0707
33-59Q
1.0863
37.016
46
1.0211
24.241
1.0290
27.288
1-0385
30.486
1.0499
33-829
1.0633
37-304
47
1.0064
24-339
1. 01 24
27.418
1.0199
30.651
1.0292
34-037
1.0405
37-56o
48
0.99175
24.409
0.99582
27-5IS
1.0015
30.784
1.0087
34-2IO
1.0178
37-778
49
0.97719
24.451
0.97947
27.582
0.98317
30.883
0.98837
34-346
o-99535
37-958
5
0.96275
24.465
0.96323
27.618
0.96500
30.946
0.96821
34-444
0.97310
38.098
Si
0.94844
24-449
0.94718
27.620
0.94700
30.974
0.94821
34-503
0.95110
38.196
52
o.9343i
24.402
0.93123
27.590
0.92922
30.966
0.92858
34-524
0.92940
38.253
53
0.92031
24-325
0.91547
27.527
0.91167
30.921
0.9091 1
34-505
0.90800
38.267
54
0.90650
24.218
0.89994
27.429
0-89433
30.839
0.88995
34-444
0.88685
38.236
55
0.89281
24.079
0.88465
27.296
0.87728
30.718
0.87106
34-342
0.86600
38.160
56
0.87938
23.910
0.86953
27.128
0.86044
30.558
0.85242
34-197
0.84555
38.039
57
0.86619
23.709
0.85471
26.924
0.84389
30.358
0.8341 1
34.008
0.82545
37.869
58
0.85319
23-475
0.84012
26.683
0.82767
30.116
0.81611
33-773
0.80570
37-65o
59
0.84044
23.209
0.82582
26.406
0.81172
29.834
0.79847
33-493
0.78630
37-382
60
0.82794
22.910
0.81176
26.091
0.7961 1
29.510
0.78121
33-i67
0.76735
37.062
61
0.81569
22.578
0.79806
25-738
0.78083
29.142
0.76437
32.792
0.74880
36.688
62
0.80375
22.212
0.78464
25-347
0.76594
28.730
o.74795
32.368
0.73070
36.261
63
0.79213
21.813
0.77159
24.917
0-75*39
28.274
0.73179
31-803
0.71300
35-778
64
0.78075
21.380
0.75888
24.447
0.73722
27.774
0.71611
3I-368
0.69575
35-238
65
0.76975
20.913
0.74647
23-938
0.72344
27.228
0.70084
30.792
0.67900
34-639
66
0.75906
20.413
0.73447
23.390
0.71006
26.636
0.68605
30.162
0.66275
33-98o
67
0.74869
19.879
0.72282
22.802
0.69711
25-997
0.67168
29.478
0.64700
33.261
68
0.73869
19.31 1
0.71159
22.175
0.68455
25-312
0.65779
28.741
0.63175
32-479
69
0.72900
18.710
0.70076
21.508
0.67244
24.580
0.64421
27.949
0.61700
31-634
70
0.71975
18.076
0.69035
20.801
0.66083
23.802
0.63153
27.102
0.60280
30.725
7i
0.71081
17.410
0.68035
20.055
0.64967
22.976
0.61916
26.199
0.58915
29.750
72
0.70231
16.712
0.67076
19.271
0.63900
22.104
0.60731
25.241
0.57605
28.709
73
0.69419
15.982
0.66165
18.448
0.62878
21.187
0.59600
24.227
o-5635S
27.602
74
0.68650
15.221
0.65300
17-588
0.61911
20.224
0.58526
23-158
0.55165
26.428
75
0.67919
14-431
0.64476
16.692
0.60994
19.215
0.57500
22.034
0.54035
25.187
76
0.67231
13-613
0.63700
15.760
0.60128
18.162
0.56542
20.856
0.52970
23.880
77
0.66588
12.767
0.62976
14.794
o.593 7
17.068
0.55637
19.625
0.51970
22.507
78
0.65988
11.894
0.62300
13-795
0.58561
15-933
Q-54795
18.343
0.51035
21.070
79
0.65431
10.997
0.61676
12.765
0.57861
I4-758
0.5401 1
17.012
0.50165
19-571
80
0.64925
10.076
0.6 1 106
11.705
0.57217
13-545
0.53295
I5-633
0.49364
18.011
81
0.64463
9-134
0.60582
10.618
0.56633
12.298
0.52642
14.209
0.48636
16.391
82
0.64050
8.171
0.601 1 2
9-505
0.56106
11.019
0.52052
12.744
0.47979
14.722
83
0.63681
7-i9i
0.59700
8.370
0.55639
9.711
0-51530
11.240
0.47396
13.000
84
0.63363
6.194
o-5934i
7.214
o.55234
8-374
0.51075
9.702
0.46888
11-233
85
0.63094
5.184
0-59035
6.039
0.54890
7-OI5
0.50689
8-133
0.46455
9.426
86
0.62875
4.161
0.58782
4.850
0.54607
5-636
0.50372
6-539
0.46101
7-584
87
0.62700
3.129
0.58586
3-649
0.54387
4.241
0.50124
4-923
0.45823
5-713
88
0.62575
2.090
0.58445
2.438
0.54229
2.834
o.49947
3.291
0.45624
3.821
89
0.62500
1.046
0.58361
1.230
o.54i35
1-419
0.49841
1.648
0.45505
1.914
90
0.62473
0.000
0.58333
0.000
0.54103
0.000
0.49805
0.000
0.45465
0.000
Example.
sinh (i.J
t a /
*/77)
: o.593i7 /
i7.o68
= 0.59317
/I7.4'.05".
[23]
Table IV. CORRECTING FACTOR.
sinh 6
e
Continued
2-3
2.4
2-5
45
1. 1043
40.558
1. 1248
44-205
I. 1480
47.946
1. 1740
5^769
1.2032
55-661
46
1.0789
40.905
1.0970
44613
I.II77
48.419
1.1411
52.312
1. 1674
56.278
47
1.0538
41.213
1.0695
44.981
I.0877
48.85I
1. 1085
52.813
1. 1320
56.852
48
1.0289
41.482
1.0423
45-307
I.O580
49.241
1.0762
53.27I
1.0972
57.383
49
1.0043
41. 711
i-oi53
45-592
I.O286
49-588
1.0444
53-685
1.0627
57.869
5
0.97986
41.898
0.98864
45-834
O.99965
49.890
1.0130
54-053
1.0288
58.309
Si
o.95576
42.042
0.96232
46.031
O.97IO4
50.146
0.98200
54-375
0.99540
58.701
52
o.93i95
42.142
0.93636 46.181
O.94283
50.354
0.95150
54.648
0.96256
59.044
S3
0.90848
42.197
0.91077
46.284
O.91504
50.5I4
0.92154
54-87I
0.93028
59-337
54
0.88533
42.205
0.88559
46.338
O.88774
50.623
0.89208
55-042
0.89860
59-578
55
0.86257
42.165
0.86082
46.342
O.8609I
50.680
0.86308
55-i6o
0.86748
59-765
56
0.84019
42.076
0.83646 46.294
O.83457
50.683
0.83467
55-223
0.83700
59.896
57
0.81819
41-935
0.81255
46.193
O.80869
50.629
0.80683
55-228
0.80712
59-970
58
0.79662
41.742
0.78909
46.035
O.78331
50.5I8
0-77954
55-174
0.77788
59.984
59
0.77543
41.494
0.76609
45.820
0.75848
50.347
0.75283
55-059
0.74932
59-936
60
o.7547i
41. 191
0-74359
45-546
0.73417
5O.II4
0.72671
54.880
0.72140
59-823
61
o.73447
40.830
0.72159
45.210
O.71043
49.816
0.70121
54.634
0.69412
59.642
62
0.71467
40.410
0.70009
44.811
O.68725
49-451
0.67633
54.3I9
0.66752
59-391
63
0.69538
39.929
0.67914
44-345
O.66465
49.016
0.65204
53-931
0.64160
59.067
64
0.67657
39-386
0.65873
43.811
O.64261
48.509
0.62838
53467
0.61636
58.665
65
0.65829
38.777
0.63886
43-207
O.62II3
47.926
0.60533
52.924
0.59176
58.182
66
0.64053
38.101
0.61955
42.529
O.60026
47.264
0.58296
52.297
0.56784
S7-6i3
67
0.62329
37-357
0.60082
41-775
O.58004
46.519
0.56121
5L583
0.54464
56.954
68
0.60657
36.542
0.58268
40.943
O.56043
45-688
0.54013
50-777
0.52208
56.198
69
0-59043
35-655
0.56514
40.029
C54I43
44.767
0.51971
49.874
0.50024
55-341
70
0.57487
34.694
0.54818
39.030
O.52309
43-752
0.49996
48.868
0.47908
54.376
7i
0.55990
33656
0.53186
37-944
0.50539
42.638
0.48088
47-754
0.45864
53-296
72
o.54557
32.541
0.51618
36.769
O.48835
41.422
0.46246
46.526
0.43888
52.092
73
0.53181
3I-348
0.50118
35-5oi
O.47204
40.100
0.44479
45-177
0.41988
50.755
74
0.51871
30.074
0.48682
34-I38
O.45644
38.667
0.42783
43-70I
0.40160
49.277
75
0.50629
28.719
0.47323
32.678
O.44152
37.II8
0.41165
42.091
0.38408
47.648
76
o.49453
27.283
0.46027
31. 119
O.42736
35-449
0.39621
40.341
0.36732
45.857
77
0.48347
25.766
0.44810
29.459
O.41397
33-659
0.38157
38.443
o-35!37
43.891
78
0.473 1 1
24.168
0.43666
27.699
O.4OI35
31-744
0.36775
36.390
0.33625
41.740
79
0.46349
22.491
0.42601
25-839
O.38963
29.701
0.35480
34.I78
0.32201
39-392
80
o.4546i
20.736
0.41617
23.879
0.37873
27-531
0.34273
3 I -8o3
0.30869
36.836
81
0.44650
18.907
0.40716
21.822
O.36873
25-233
0.33162
29.261
0.29633
34-063
82
0.43919
17.008
0.39902
19.671
0-35965
22.810
0.32149
26.550
0.28500
3 J -o65
83
0.43268
15-043
0.39176
17-432
0.35I53
20.267
0.31239
23.676
0.27477
27.841
84
0.42699
13-015
0.38540
15. in
O.3444I
17. 611
0.30438
20.643
0.26569
24.390
85
0.42215
10.933
o.37998
12.715
0.3383I
14.851
0.29748
17.462
0.25784
20.723
86
0.41818
8.806
o-3755i
10.254
0.33328
12.000
0.29178
14-147
0.25131
16.855
87
0.41507
6.639
0.37202
7.740
0.32933
9.071
0.2872.8
10.717
0.24614
12. 811
88
0.41284
4-443
0.36951
5-183
O.32650
6.082
0.28405
7.197
0.24241
8.624
89
0.41 1 50
2.226
0.36800
2-599
0.32479
3-051
0.28210
3-6i5
0.24014
4.338
90
0.41 105
0.000
0.36750
0.000
O.32422
0.000
0.28144
0.000
0.23939
0.000
Example.
sinh (2.
3 /84)
/8,o
= 0.3444I |
/i7.6n
= 0.34441
/i7-36'
4O .
[24]
Table IV. CORRECTING FACTOR.
sinh 6
e
Continued
2.6
2.7
2.8
45 1-2354
46 1. 1967
47 1. 1586
48 1. 1209
49 1.0838
50 1.0473
51 1.0113
52 0.97608
53 0.94145
54 0.90750
0.87419
0.84162
0.80973
0.77854
0.74808
0.71835
0.68935
0.66104
0.63346
0.60662
0.58054
o.555i9
0-53054
0.50658
0.48338
70 0.46089
71 0.439 1 1
72 0.41808
73 0.39773
74 0.37814
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
75
76
77
78
79
85
86
87
88
89
0.35930
0.34123
o.32395
0.30749
0.29189
80 0.27718
81 0.26346
82 0.25078
83 0.23922
84 0.22887
0.21986
0.21227
0.20623
0.20184
0.19917
59-013
60.307
60.957
61.564
62.126
62.641
63.109
63.528
63.897
64.214
64.476
64.684
64.834
64.925
64.954
64.918
64.816
64.644
64.399
64.077
63.674
63.185
62.606
61.930
61. 151
60.262
59-254
58.117
56.841
55-414
53-822
52.049
50.079
47.893
45-471
42.793
39.837
36.583
33.016
29.126
24.910
20.382
I5-57I
10.524
5-307
1. 2710
1.2293
1.1881
1. 1476
1. 1077
1.0685
1 .0300
0.99219
0.955H
0.91881
0.88333
0.84863
0.81467
0.78152
0.74919
0.71767
0.68692
0.65700
0.62786
o.59952
o.57i93
0-545*4
0.51911
0.49386
0.46937
0.44559
0.42256
0.40026
0.37872
0.35789
0.33780
0.31846
0.29987
0.28206
0.26507
0.24894
0.23374
0.21954
0.20644
0.19458
0.18409
0.16794
0.16264
0.15938
63.614
64.386
65.116
65.801
66.442
67.037
67-585
68.084
68.532
68.929
69.274
69-563
69.797
69-973
70.088
70.140
70.128
70.047
69.895
69.669
69.364
68.978
68.504
67-935
67.266
66.489
65596
64.576
63-415
62.101
60.617
58.943
57-058
54-935
52-542
49.847
46.812
43-396
39-554
35-252
30.458
25.164
19.390
I3.I94
6.682
1.3102
1.2652
1.2209
1. 1774
1-1345
1.0925
1-0513
1.0109
0.97143
0.93279
0.89500
0.8581 1
0.82211
0.78700
o-75275
0.71943
0.68700
0.65543
0.62475
o.59493
0.56596
0.53785
0.51054
0.48404
0.45832
0-43343
0.40928
0.38586
0.36321
0.34125
0.32002
0.29951
0.27971
0.26064
0.24231
0.22476
0.20804
0.19222
0.17741
0.16375
0.15142
0.14069
0.13184
0.12520
0.1 2 105
67.653
68.506
69-3I7
70.084
70.806
71-483
72.113
72.694
73.226
73.708
74-I38
74-515
74-837
75-103
75-3"
75-459
75-544
75-565
75-5I9
75-403
75.214
74.948
74-599
74.164
73.634
73005
72.267
71.411
70.424
69.292
67.996
66.516
64.827
62.897
60.686
58.145
55-217
5I.833
47.908
43-351
38.066
31.968
25-015
17.244
8.809
2.9
o
I-353Q 71-721
1.3046 72.658
1.2570 73-551
1. 2 103 74.400
1-1644 75-205
3-o
1.1195
I-0755
1.0324
0.99038
0.94928
0.90917
0.87007
0.83197
0.79487
0.75876
0.72366
0.68955
0.65641
0.62424
0.59303
0.56272
o.53334
0.50486
0.47724
0.45045
0.42448
0-39934
0-37497
o.35i35
0.32845
0.30627
0.28478
0.26397
0.24379
0.22432
0.20551
0.18738
0.16998
O.I5343
0.13774
75-965
76.670
77-345
77.963
78.532
79.050
79.5I7
79.932
80.293
80.598
80.847
81.037
81.167
81.235
81.239
81.176
81.044
80.838
8o.555
80.190
79.738
79.191
78.541
77.780
76.894
75-867
74.680
73.309
71.721
69.876
67.721
65.183
62.169
58.553
54-168
0.12323 48.795
0.11016 42.168
0.098934 34-005
0.090148 24.110
0.084469 12.576
I-399S
1-3475
1.2965
1.2465
1. 1974
75.8i4
76.832
77.808
78.741
79.630
80.474
81.272
1. 1494
1-1025
1.0567 82.024
1.0120 82.729
0.96837 83.386
83.994
84-553
85.062
85.510
85.924
86.276
86.574
86.817
87.004
87-I33
87.204
87.214
87.161
87.043
86.858
86.602
86.271
85.860
85-363
84.772
0.29674 84.077
0.27452 83.265
0.25296 82.319
0.23202 81.216
0.21168 79.925
0.19191 78.404
0.17270 76.592
0.15404 74.404
O.I3596 71-709
0.1 1849 68.313
0.10174 63.903
0.085917 57-974
0.071443 49-70I
0.059103 37.843
0.050307 21.091
0.92590
0.88453
0.84433
0.80523
0.76727
0.73040
0.69463
0.65993
0.62630
0-59373
0.56217
0.53160
0.50203
0.47340
0.44567
0.41883
0.39283
0.36767
0.34327
0.31964
90 0.19827 0.000 0.15829 0.000 0.11964 0.000 0.082845 0.000 0.047040 0.000
Example.
sinh (3.0 /86)
3-Q 786
= 0.085917 /57-974 - 0.085917 /59..s8 , .26 r .
[25]
/
Table V. CORRECTING FACTOR.
tanhg
e
- r/y
o-3
0.4
0.5
45
1. 00000
O.I88
O.99985
0.765
0-99937
1. 718
0.99803
3-046
0.99514
4-75
46
I.OOOIO
O.I88
I.OOO3O
0.764
1.00040
1.719
0.99988
3055
0.99804
4-771
47
1. 0002 1
O.I88
I.OOO75
0.763
1. 00143
1.720
1.00173
3.058
1.00094
4.781
48
1.00033
0.188
I. OOI 20
0.761
1.00250
1. 717
1.00358
3.058
1.00384
4.787
49
1.00044
O.187
I.00I70
0.758
1-00357
1. 710
1.00543
3-053
1.00680
4.787
So
1.00056
O.187
I.OO215
o.755
1 .00460
1-703
1.00733
3.045
1.00980
4.780
5i
1.00068
O.187
I.OO265
0.749
1.00563
1.694
1.00925
3031
1.01278
4.767
52
1.00080
O.I86
I.OO3 IO
o.744
1.00670
1.685
1.01115
3.014
1-01578
4-747
53
1.00092
O.184
I -00355
0.738
1.00773
1.672
1. 01303
2-995
1.01878
4.724
54
1.00103
O.182
I .OO405
0.732
1.00877
1.656
1. 01 490
2.969
1. 02 1 78
4.692
55
1.00114
O.180
I.OO45O
0.724
1 .00980
1.638
1-01675
2.942
1.02478
4656
56
1.00125
O.I77
I.OO495
0.715
1. 01083
1.618
1.01865
2.91 1
1.02778
4.612
57
1.0013s
O.I75
I-OOS35
0.705
1.01183
1.596
1.02050
2.876
1.03076
4.561
58
1.00146
O.I72
1-00575
0.694
1.01283
1-574
1.02230
2.836
1-03374
4506
59
1.00156
O.17O
1.00620
0.682
1.01380
1.548
1.02410
2-793
1.03670
4.444
60
1. 001 7
O.167
1.0067
0.668
1.0148
1.521
1.0259
2-745
I-0397
4-375
61
1.0018
O.163
1.0070
0.655
1.0158
1.490
1.0278
2.695
1.0425
4-300
62
I.OOIQ
O.I59
1.0074
0.640
1.0167
1.458
1.0294
2.641
1.0454
4.220
63
1.0020
O.I55
1.0078
0.625
1.0176
1.425
1-0311
2.583
1.0482
4-133
64
1.0020
O.I5I
1.0082
0.609
1.0185
1.390
1.0328
2.521
I.05 10
4.041
65
I.002I
0.147
1.0086
0.592
1-0193
1-353
1.0344
2.456
1-0538
3-942
66
I.0022
0.143
1 .0090
0-575
1.0202
I-3I4
1.0360
2.388
1.0564
3.836
67
I.OO23
O.I38
1.0093
o.557
1.0210
1-273
1.0376
2.315
1-0591
3-724
68
I.OO24
O.I34
1.0097
0-539
1. 0218
1. 231
1.0391
2.240
1. 0617
3609
69
I.OO25
O.I29
I.OIOO
0.520
1.0226
1. 187
1 .0406
2.163
1.0642
3 489
70
I.OO26
O.I23
I. 0103
0.499
1.0234
1. 141
1.0420
2.082
1.0666
3-362
7i
I.OO26
O.Il8
1. 0106
0.478
1.0241
1.094
1 -0434
1.998
1.0689
3229
72
I.OO27
0.II2
I. 0109
0.456
1.0247
1.045
1.0447
1. 91 1
1.0712
3.091
73
I.OO28
O.I07
I.OII2
0-434
1.0254
o.995
1 .0460
1. 82 1
1 -Q734
2.948
74
I.OO28
0.102
I.OII4
0.41 1
1.0260
0.944
1.0472
1.728
i-o755
2.800
75
I.OO29
O.O96
I.OII7
0.388
1.0266
0.892
1.0483
1.632
1.0774
2.649
76
I.OO29
0.090
I. OI 20
0.365
1.0272
0.838
1.0494
1-534
1.0793
2493
77
I.OO3O
O.084
I.OI22
0.341
1.0277
0.783
1.0504
1-434
1. 081 1
2333
78
I.OO3O
O.078
I.OI23
0.316
1.0282
0.727
1-0513
1-332
1.0828
2.169
79
I. OO3 1
0.072
I.OI25
0.291
1.0287
0.671
1.0522
1.229
1.0843
2.001
80
I. OO3 1
O.066
I.OI27
0.266
1.0291
0.614
1-0530
1. 124
1.0857
1.830
81
I.OO32
O.060
I.OI29
0.241
1.0295
0-555
1-0538
1.017
1.0870
1.656
82
I.OO32
0.054
I.OI3O
0.215
1.0298
0.494
1.0544
0.908
1. 0881
1.480
83
I.OO32
0.047
I.OI32
0.188
1.0301
0-433
1.0550
0.797
1.0892
1.301
84
I.OO33
O.O4O
I-OI33
0.162
1.0304
0.372
1-0555
0.685
1. 090 1
1. 119
85
I.OO33
O.O33
I-OI34
0.136
1.0307
0.3 1 1
1.0560
o.573
1 .0908
0935
86
I.OO33
0.026
I-OI34
0.109
1.0309
0.249
1-0563
0.460
1.0914
0.749
87
I.OO33
0.OI9
i-oi35
0.082
1. 03 10
0.187
1.0566
0.346
1. 0919
0.562
88
I-0033
O.OI2
i-oi35
0.054
1-0311
0.125
1.0568
0.232
1.0923
0-374
89
I.OO33
0.006
i-oi35
0.027
1-0311
0.063
1.0570
0.117
1.0926
0.187
90 1.0033 0.000 1.0136 0.000 1.0311 0.000 1.0570 0.000 1.0926 0.000
Note.
Example.
Negative quantities are in heavy type,
tanh (0.4 /74)
Q-4 /74
= 1.0472 \i.728 = 1.0472 \i.43'.4i"
[26]
Table V. CORRECTING FACTOR.
tanh 6
e
= r /y. Continued
0.6
0.7
0.8
0.9
45 0.99010
6.817 0.98189
9.214
0.96971
II.902
O.95284
14-839 0.93077
17956
46 0.99417
6.854 0.98727
9.281
0.97646
I2.020
O.96089
15.020 0.93999
18.216
47 0.99830
6.881 0.99279
9-337
0-98339
12.122
O.9692I
15-185 0.94950
18.461
48 l
.00248
6.901 0.99840
9383
0.99050
I2.2IO
0.97779
15-334 0.95938
18.692
49 1
.00672
6.912
.00410
9.419
0.99780
12.285
O.9866S
15-469 0.96966
18.908
50 l
.01100
6.915 l
.00991
9-443
1.00526
12.347
O.99578
15-588 0.98032
19.108
5i I
I 533
6.908 ]
.01581
9-455
i.o[289
12.395
i.oo5[8
15.690 0.90136
19.290
52 1
.01970
6.893 3
.02181
9-457
1.02069
12.427
1. 01486
15-777 J
.00282
19-455
53 1
.02412
6.870 ]
.02789
9-445
1.02864
12.444
1.02479
15.845 1
.01469
19.600
54 1
.02855
6.838 1
03403
9-423
1.03675
I2.446
1.03500
I5.895 1
.02697
19.726
55 >
.03300
6.797 1
.04024
9.388
1. 04501
12.432
1.04549
15925 1
03970
19.828
56 l
03747
6.746 3
[.04653
9-338
1-05343
I2.40I
1.05626
15-934 1
05287
19.909
57 >
04195
6.685 1
.05286
9-275
1.06196
12.353
1.06729
15922 ]
.06648
19.965
58 1
.04642
6.616
[.05921
9.200
1. 07061
12.288
1.07854
15.889 I
.08054
19.996
59 1
.05089
6.537 1
[.06561
9.112
1.07939
12.203
1.09007
I5.833 1
.09506
19.998
60 1
05537
6.448
[.07210
9.010
1.08829
12.100
1.10188
15-753 !
[.11009
19.973
61 i
[.05980
6.350
[.07856
8.893
1.09726
II.978
1.11390
15.647
[-12555
19.918
62 ]
[.06420
6.242
[.08500
8.762
1. 10630
11.835
1.12614
I5.5I4
[.14144
19832
63 1
[.06858
6.124
[.09143
8.617
1.11540
11.673
1.13856
15-355
[-15777
19.711
64 1
[.07293
5998
[.09783
8.458
1. 1 2456
II.49I
1.15116
15.169
[-17454
19-555
65
[.07722
5.862 ]
[.10420
8.285
1. 13373
11.288
1. 16392
14.956
[.19173
19362
66 ]
[.08143
5.7I6
[-II053
8.098
1.14291
II.064
1.1 7684
14.711
[.20935
19.131
67 J
.08560
5561
[.1 1683
7.895
1. 15208
IO.82O
1. 1 8989
14.438
[.22737
18.860
68 :
.08967
5-397
[.12299
7.678
1.16118
10.552
1.20298
14132
[.24569
18.545
69
[.09363
5223
[.12904
7-447
1. 17020
IO.263
1. 21608
13-796
[.26429
18.188
70 i
09750
5.041
[.13500
7.202
1. 179*5
9-953
1. 22919
13.428
[.28316
17.785
7i
[.10125
4-850
[.14083
6-943
1. 18796
9.621
1.24226
13.026
[.30221
17-334
72 i
.10490
4650
[.14651
6.671
1. 19659
9.268
1-25524
12.592
[.32140
16.836
73 i
.10842
4.441
[.15201
6.386
1.20503
8.894
1.26807
12.126
[.34063
16.290
74
[.11180
4.225
[-15734
6.087
1. 21325
8-499
1.28067
11.628
[.35986
I5-693
75
1-11503
4.002
[.16244
5-775
1.22121
8.083
1.29300
11.097
[.37894
15-043
76
[.11810
3.772
[.16733
5-450
1.22889
7.648
1.30500
10.532
[-39775
14.342
77
[.12102
3-534
[.17197
5-"4
1.23623
7.192
1-31659
9936
[.41620
13-591
78
M2375
3289
[.17636
4.767
1. 24319
6.718
1.32772
9-309
[.43412
12.788
79
[.12628
3038
[.18046
4.409
1.24976
6.227
1-33830
8.653
[.45141
11-935
80
r. 1 2863
2.781
[.18427
4.042
i-2559i
5.7i8
1.34827
7.966
[.46790
11.032
81
1. 13078
2.519
[.18777
3.666
1. 26158
5-195
1-35754
7-254
[.48345
10.081
82
[.13273
2.251
[.19094
3-281
1.26674
4656
1.36607
6.517
[.49790
9.087
83
[-I3447
1.979
[.19377
2.888
1.27138
4.104
1.37378
5-757
[.51110
8.052
84
t.i3598
1.704
[.19626
2.488
1-27545
3.540
1.38059
4-975
[.52289
6.977
85
[.13727
1.425
[.19839
2.083
1.27895
2.966
1.38646
4-175
[53314
5.868
86
[.13832
1. 144
[.20013
1.672
1.28185
2.383
1.39132
336o
[54170
4-731
87
M39 x 5
0.860
[.20150
1-257
1. 28413
1.794
i.395i8
2.532
[.54848
3-571
88
[-13975
o.574
[.20247
0.839
1-28575
1. 199
1-39793
1.692
[-55339
2.391
89
1.14010
0.287
[.20306
0.420
1. 28671
0.600
1-39959
0.847
[55637
1. 198
90
1.14022
0.000
[.20327
0.000
1.28700
0.000
1. 4001 7
0.000
[-55740
0.000
Note.
Negat
ive quantities are in heavy type.
*
1
? .xamnle.
tanh 1
Q-9 /75
')
= I.2Q3
= 1.20.3 \
\lI.OQ7
n.O5'.40"
Q-9 /75
[27]
Table V. CORRECTING FACTOR.
tanh d
e
fy. Continued
i-3
1.4
i-5
45
0.90354
21.167 0.87142
24.384
0.83515
27536
0-79593
30.516
0.75487
33-288
46
o.9i359
21.524 0.88183
24.856
0.84561
28.118
0.80600
31.225
0.76427
34116
47
0.92400
21.869 0.89275
25315
0.85661
28.699
0.81664
31936
0.77420
34-952
48
0.93482
22.201 0.90425
25.764
0.86815
29.279
0.82786
32.648
0.78467
35-792
49
0.94618
22.520 0.91625
26.202
0.88038
29.852
0.83971
33360
0-79573
36.638
So
0.95809
22.822 0.92892
26.629
0.89331
30.416
0.85228
34.070
0.80747
37-490
5i
0.97055
23.109 0.94225
27.043
0.90685
30.973
0.86557
34-778
0.81993
38.348
52
0.98345
23-379 0.95617
27.442
0.92123
31521
0.87964
35-485
0.83320
39-213
53
0.99700
23.630 0.97083
27.826
0.93638
32.059
0.89457
36.189
0.84727
40.086
54
I.OIII
23.861 0.98625
28.193
0.95238
32.586
0.91043
36.890
0.86220
40.965
55
1.0258
24.070
[.0025
28.540
0.96938
33100
0.92729
37.587
0.87813
41.849
56
1. 041 2
24.256
[.0196
28.867
0.98738
33-599
0.94529
38.279
0.89513
42.738
57
1.0572
24.417
1-0375-
29173
1.0065
34.082
0.96443
38.964
0.91333
43634
58
1.0739
24-551
[.0564
29.454
1.0266
34-548
0.98479
39642
0.93280
44-534
59
1. 09 14
24.657
[.0763
29.708
1.0482
34-993
1.0066
40.311
0.95367
45-441
60
1. 1096
24-733
[.0973
29.932
1.0710
35-416
1. 0301
40.968
0.97613
46.349
61
1. 1286
24.774
[.1195
30.124
I-0953
35-813
1-0551
41. 611
1 .0003
47.262
62
1. 1484
24.778
t.1428
30.280
1.1212
36.180
1.0820
42.239
1.0264
48.176
63
1. 1689
24-745
[.1674
30.397
1. 1488
36.515
1.1 109
42.850
1.0546
49092
64
1. 1904
24.672
[-I934
30.473
1. 1784
36.814
1.1421
43-438
1. 085 1
50.009
65
1. 2126
24-554
[.2208
30.502
1.2099
37-072
I-I759
44.001
1.1184
50.924
66
1-2357
24.388
[.2496
30.480
1.2436
37-285
1. 2124
44-535
1. 1546
51-834
67
1.2596
24-173
[.2799
30.403
1.2798
37-446
1.2520
45-034
1 -1943
52.739
68
1.2845
23.904
r.3119
30.263
1-3185
37-548
1-2951
45-493
1.2377
53.636
69
1.3101
23-579
c-3457
30.059
1.3600
37-585
1.3420
45.904
1.2857
54-520
70
I-3365
23.194
c.3811
29.781
1 .4046
37-548
1-3933
46.260
I-3385
55.388
7i
1-3637
22.744
[.4183
29.425
1.4525
37-430
1-4495
46.552
1-3973
56.235
72
I-39I5
22.227
[-4573
28.983
I-5039
37-2i8
i-5"3
46.768
1.4628
57.056
73
1.4200
21.639
[.4981
28.447
1-5592
36.899
1-5794
46.894
1-5362
57.84I
74
1.4489
20.978
[-5407
27.810
1.6186
36.461
1.6546
46.916
1. 6190
58.581
75
1-4783
20.238
[.5849
27.064
1.6822
35-890
1.7380
46.814
1. 7129
59.266
76
I-5077
19.419
[.6307
26.202
I-7505
35-I7Q
1.8308
46.567
1.8202
59.880
77
1-5373
18.518
[.6778
25.214
1-8235
34.280
I-934I
46.145
1.9438
60.403
78
1.5665
17-532
t.7261
24.094
1. 9012
33-202
2.0498
45-514
2.0875
60.814
79
1-5955
16.462
[-7749
22.835
I-9835
31-912
2.1792
44-633
2.2562
61.076
80
1.6235
15.308
[.8239
21.429
2.0702
30.389
2.3240
43-454
2.4563
61.144
81
1-6505
14.069
[.8726
19.874
2.1604
28.609
2.4862
4I-9I5
2.6973
60.956
82
1-6759
12.748
[.9200
18.168
2.2531
26.553
2.6669
39-944
2.9917
60.422
83
1.6996
11.350
t.9654
16.310
2.3466
24.200
2.8668
37-454
3-3577
59.412
84
1. 7212
9.879
2.0078
14.306
2.4388
21.540
3.0848
34-354
3.8207
57.724
85
1.7402
8.343
2.0463
12.164
2.5267
18.568
3-3 l6 4
30.541
4.4198
55.045
86
1.7562
6.748
2.0796
9.898
2.6065
15.294
3-5521
25-931
5.2010
50.866
87
1. 7691
5-105
2. I068
7-525
2.6744
11.747
3-7765
20.477
6.2275
44-356
88
I-7785
3.425
2.I269
5.067
2.7266
7.970
3-9665
14.214
7.5060
34-274
89
I-7843
1.719
2-1393
2.548
2.7596
4.029
4.0952
7-293
8.7880
19.305
90
1.7862
0.000
2-1434
0.000
2.7709
0.000
4-I4I3
0.000
9.4007
0.000
Note. Negative quantities are in heavy type
tanh (1.3 /45 )
Example.
i-3 /4S!
= 0.83515 \27.536 = 0.83515 \i7.32'.io".
[28]
Table V. CORRECTING FACTOR.
tanhfl
e
1.6
i-7
1.8
= r Ay. Continued
1.9
45
0.71331
35-799
0.67224
38.016
0.63250
39-937
0.59484
41562
0-55955
42.906
46
0.72175
36.733
0.67959
39-048
0.63883
41-050
0.60005
42.740
0.56375
44.133
47
0.73069
37-682
0.68741
40.098
0.64544
42.186
0.60553
43.942
0.56815
45.387
48
0.74013
38.642
0.69565
41.166
0.65239
43-341
0.61126
45-i68
0.5727S
46.667
49
0.75013
39-615
0.70435
42.251
0.65978
44-520
0.61726
46.422
0.57750
47-977
50
0.76069
40.600
0-7I359
43-355
0.66756
45-725
0.62358
47-705
0.58250
49-319
5i
0.77194
41.600
0.72329
44.480
0.67572
46.955
0.63026
49.019
058770
50.694
52
0.78381
42.616
0.73365
45.627
0.68433
48.213
0.63721
50.366
0-593I5
52.103
53
0.79650
43-646
0.74465
46.797
0.69350
49-50I
0.64458
51-747
0.59885
53-550
54
0.81000
44.691
0.75629
47.992
0.70317
50.820
0.65232
53.i65
0.60480
55-039
55
0.82438
45-754
0.76865
49.212
0.71344
52.174
0.66047
54-621
0.61100
56.571
56
0.83969
46.834
0.78188
50.461
0.72433
53.564
0.66911
56.121
0.61750
58.149
57
0.85613
47-931
0.79600
51-739
0.73594
54.992
0.67821
57-666
0.62435
59-777
58
0.87369
49.047
0.81 106
53-047
0.74828
56.460
0.68784
59-259
0.63150
61.458
59
0.89256
50.183
0.82724
54389
0.76144
57-974
0.69805
60.905
0.63905
63-I95
60
0.91288
51-339
0.84459
55-768
0.77550
59-535
0.70895
62.606
0.64695
64.995
61
o.93475
52.516
0.86324
57.181
0.79056
61.145
0.72047
64.366
0.65530
66.860
62
0.95834
53-714
0.88335
58.635
0.80672
62.810
0.73274
66.191
0.66405
68.793
63
0.98394
54-935
0.90506
60.131
0.82406
64-533
0.74579
68.085
0.67330
70.802
64
1.0117
56.181
0.92853
61.674
0.84272
66.318
0.75974
70.052
0.68310
72.891
65
1. 0419
57-452
0.95400
63.266
0.86283
68.172
0.77463
72.099
0.69340
75-o68
66
1.0749
58.748
0.98176
64.910
0.88461
70.098
0.79063
74.232
0.70430
77.338
67
i.iiii
60.072
1.0121
66.613
0.90817
72.104
0.80774
76.459
0.71585
79.707
68
1. 1508
61.425
1 -04 53
68.376
0.93372
74.196
0.82611
78.786
0.72810
82.184
69
1. 1948
62.809
1. 081 7
70.209
0.96156
76.382
0.84579
81.221
0.74105
84.776
70
1-2433
64.224
1.1219
72.116
0.99189
78.671
0.86705
83-773
0.75475
87.490
7i
1.2974
65.674
1. 1663
74.106
1.0251
81.074
0.88989
86.454
0.76925
90.337
72
i.358o
67.160
1. 2157
76.187
1. 0614
83.602
0.9I453
89.273
0.78465
93326
73
1.4262
68.686
1.2708
78.371
1.1013
86.266
0.941 1 1
92.244
0.80095
96.466
74
^OSS
70.256
I.3325
80.670
1. 1452
89.084
0.96974
95-379
0.81815
99.769
75
i-59i3
71.873
1.4020
83.101
1. 1936
92.076
1 .0005
98.692
0.83625
103.245
76
1.6924
73-543
1.4807
85.685
1.2470
95-261
1 -033 7
102.202
0.85525
106.905
77
1.8098
75-274
I.5704
88.447
1. 3061
98.664
1.0693
105.925
0.87515
110.760
78
1-9473
77.078
1.6731
91.420
I-37I4
102.315
1. 1074
109.881
0.89585
114.820
79
2.1104
78.966
1-191$
94.644
1.4436
106.250
1. 1478
114.088
0.91720
119.093
80
2.3068
80.960
1.9288
98.175
I.523I
110.510
1. 1906
118.568
0.93905
123.590
81
2-5472
83.087
2.0894
102.083
1.6104
115-140
1-2352
123-344
0.96110
128.319
82
2.8474
85-390
2.2775
106.466
1.7056
120.191
1. 2813
128.428
0.98305
133-281
83
3.2326
87-937
2.4992
1 1 1.446
1.8078
125.722
1.3279
133-842
1.0045
138.474
84
3-7435
90.839
2.7604
117.199
I-9I55
131-793
1-3739
139590
1.0249
I43.894
85
4.4502
94.289
3.0648
123.945
2.0255
138.448
I-4I79
I45.673
1.0436
149.528
86
5-4825
98.668
3-4"4
I3L956
2.1329
145-720
1-4579
152.075
1. 060 1
155-359
87
7-H75
104.791
3-7856
141.527
2.2309
153.606
1.4921
158.768
1.0738
i6i.359
88
9.9938
114.760
4.1472
152.868
2.3107
162.043
1-5184
165.700
1.0840
167.494
89
15.528
I35-OII
4-423I
165.896
2.3628
170.905
1-5349
172.805
1.0904
I73.723
90
21-395
180.000
4-5275
180.000
2.3813
180.000
1.5406
180.000
1.0925
180.000
Note.
Example.
Negative quantities are in heavy type
tanh (2.0 /8o)
2.0 /8o
= 0.93905 \i23.59Q = 0.93905 \i23.35'.24".
[29]
Table V. CORRECTING FACTOR.
tanh fl
e
r ly. Continued
2-3
2.4
2.5
45
0.52690
43-993
0.49691
44-845
0.46952
45-492
0.44467
45961
0.42212
46.283
46
0.53019
45-254
0.49941
46.127
0.47139
46.783
0.44592
47.252
0.42292
47-564
47
0.53362
46.542
0.50200
47.436
0.47322
48.101
0.44717
48.567
0.42368
48.868
48
o.537i4
47-859
0.50465
48.774
0.47509
49.446
0.44842
49.908
0.42440
50.195
49
0.54081
49.206
0.50732
50.142
0.47696
50.820
0.44958
51.277
0.42504
5L548
5
0.54462
50.586
0.51009
51-542
0.47883
52.226
0.45075
52.676
0.42560
52.929
Si
0.54852
52.001
0.51291
52.978
0.48070
53-666
0.45188
54-I07
0.42612
54-340
52
o.55257
53-452
0.51578
54-452
0.48256
55-144
0.45292
55-572
0.42652
55.782
53
0.55681
54-943
0.51868
55-965
0.48443
56.659
0.45392
57-073
0.42684
57.256
54
0.561 14
56.476
0.52168
57-520
0.48630
58.215
0.45488
58.614
0.42704
58.766
55
0.56562
58.055
0.52473
59.120
0.48813
59815
0.4557I
60.196
0.42712
60.314
56
0.57029
59.682
0.52782
60.769
0.48991
61.462
0.45646
61.822
0.42708
61.903
57
o.575H
61.361
0.53095
62.469
0.49170
63.160
0.45713
63.496
0.42688
63-534
58
0.58014
63.094
o.534i4
64.226
0.49339
64.912
0.45767
65.220
0.42648
65.211
59
0.58533
64.888
o.53736
66.042
0.49504
66.722
0.45804
66.998
0.42588
66.938
60
0.59071
66.745
0.54064
67.921
0.49661
68.594
0.45829
68.835
0.42512
68.718
61
0.59629
68.671
0-5439S
69.869
0.49813
70.531
0.45838
70.735
0.42412
70.556
62
0.60210
70.669
0.54732
71.889
0.49957
72.540
0.45829
72.701
0.42288
72.455
63
0.60814
72.744
0.55073
73.988
0.50087
74.625
0.45800
74-740
0.42140
74.419
64
0.61443
74.902
0.55418
76.171
0.50209
76.791
0-45750
76.855
0.41960
76.455
65
0.62090
77.151
0.55764
78.443
0.50317
79.044
0.45675
79-053
0.41752
78.567
66
0.62767
79.496
0.56109
80.810
0.50413
81.390
0-45579
81.341
0.41512
80.761
67
0.63471
81.942
0.56459
83280
0.50491
83.836
0.45454
83-723
0.41240
83.044
68
0.64205
84.499
0.56814
85.858
0.50557
86.389
0.45300
86.208
0.40928
85.424
69
0.64962
87.172
0.57164
88.552
0.50604
89.056
0.451 21
88.802
0.40580
87.906
70
0.65752
89.968
o.575i8
91-370
0.50630
91.843
0.44913
91514
0.40196
90.500
7i
0.66571
92.898
0.57873
94-319
0.50639
94-759
0.44671
94-352
0.39771
93-215
72
0.67424
95-968
0.58223
97-405
0.50626
97.811
0.44396
97324
0.39306
96.061
73
0.68305
99.185
0.58568
100.636
0.50596
101.006
0.44092
100.439
0.38802
99.048
74
0.69214
102.560
0.58914
104.020
0.50543
104.352
0.43754
103.706
0.38260
102.187
75
0.70152
106.099
o.59255
107.564
0.50470
107.858
0.43388
107.134
0.37681
105.489
76
0.71114
109.811
0.59586
in. 274
0.50378
"I-53I
0.42992
110.730
0.37068
108.966
77
0.72096
113.702
0.59914
115-156
0.50265
"5-374
0.42575
II4-505
0.36427
112.633
78
0.73086
117.778
0.60232
119.212
0.50135
1 19-392
0.42138
118.467
0.35762
116.501
79
0.74090
122.043
0.60536
123.446
0.49991
I23-590
0.41683
122.620
0.35080
120.582
80
0.75086
126.501
0.60832
127.859
0.49835
127.968
0.41221
126.968
0.34392
124.887
81
0.76067
131-151
0.61 109
132.449
0.49674
132.527
0.40759
I3I-5I7
0.33706
129.427
82
0.77019
135989
0.61364
137.212
0.49509
137264
0.40305
136.267
0.33033
134.209
83
0.77924
141.011
0.61600
142.140
0.49343
142. 171
0.39869
141. 212
0.32391
139-233
84
0.78767
146.210
0.61814
147.223
0.49183
147-237
0.39463
146.344
0.31790
144.499
85
0.79524
I5L570
0.62000
152.449
0.49039
152.450
0.39094
151-650
0.31248
149.994
86
0.80176
157.070
0.62155
157.800
0.48913
157-793
0.38775
I57-II3
0.30778
155-703
87
0.80710
162.690
0.62282
163.254
0.48804
163.245
0.38516
162.710
0.30396
161.598
88
0.81 100
168.406
0.62374
168.790
0.48726
168.781
0.38325
168.413
0.301 13
167.645
89
0.81338
174.187
0.62427
174.381
0.48678
174.376
0.38207
174.188
0.29940
173.796
90 0.81424 180.000 0.62445 180.000 0.48661 180.000 0.38167 180.000 0.29880 180.000
Note
Negative quantities are in heavy type.
tanh (2.3 /go")
Example. = 0.48661 V^ = 0.48661 A 80
2-3 /90
[30]
Table V. CORRECTING FACTOR.
tanhg
= r ly. Continued
2.6
2.7
2.8
2.9
3-o
45
0.40173
46.480
0.38326
46.576
O.36657
46.595
o.35i45
46.554
0.33770
46.468
46
0.40215
47-744
0.38341
47.821
O.3665O
47.8l6
0.35121
47-748
0.33733
47.637
47
0.40250
49.030
0.38348
49083
O.36632
49-051
0.35086
48.955
0.33690
48.815
48
0.40281
50.337
0.38344
50.365
O.36607
50.303
0.35045
50.175
0.33637
50.002
49
0.40304
51.667
0-38333
51.666
O.3657I
51.572
0-34997
51.409
0.33573
51.198
So
0.40319
53.022
0.383 1 1
52.988
0.36525
52.857
0.34928
52.656
0.33497
52.405
Si
0.40319
54-403
0.38278
54-332
O.36464
54-l60
0.34848
53-yi6
0.33410
53.622
52
0.40308
55-812
0.38233
55-7oo
O.36389
55483
o.34759
55.191
0.33307
54.849
53
0.40288
57.250
0.38174
57-094
O.363OO
56.826
0.34652
56.481
0.33191
56.086
54
0.40254
58.717
0.38096
58.513
O.36196
58.190
0.34528
57.788
0.33058
57.334
55
0.40200
60.219
0.38000
59-959
0.36075
59-577
0.34386
59-H2
0.32907
58.593
56
0.40131
61.756
0.37889
6i.437
0-35932
60.987
0.34226
60.452
0.32737
59862
57
0.40046
63331
O.37750
62.945
0.35768
62.422
0.34043
61.810
0.32546
61. 141
58
0.39942
64.947
0.37600
64.487
0.35580
63.884
0.33837
63.186
0.32332
62.432
59
0.39812
66.606
0.37422
66.066
0.35367
65-374
0.33602
64.582
0.32093
63735
60
0.39658
68.313
0.37215
67.684
0.35126
66.895
o.33345
65.999
0.31827
65.049
61
0.39481
70.069
0.36980
69343
0.34856
68.449
0.33056
67-439
0.31532
66.375
62
0.39273
71.879
0.36716
71.048
0.34554
70.036
0.32734
68.904
0.31206
67.713
63
o.39 35
73-747
0.36416
72.801
0.34217
71.660
0.32378
70.392
0.30847
69.063
64
0.38765
75-677
0.36081
74.607
0.33843
73.325
0.31985
71.907
0.30451
70.426
65
0.38458
77.675
0.35709
76.470
0.33430
75-033
0-31552
73-452
0.30016
71.801
66
0.38115
79-747
0.35296
78.393
0.32974
76.789
0.31076
75-027
0.29539
73.192
67
o.37733
81.898
0.34841
80.383
0.32474
78.599
0.30556
76.639
0.29018
74598
68
0.37310
84.136
o.3434i
82.449
0.3I927
80.464
0.29988
78.289
0.28450
76.021
6q
0.36844
86.469
o.33794
84-597
0.3I33I
82.396
0.29369
79.982
0.27832
77.463
70
o.36333
88.902
0.33198
86.833
0.30683
84.399
0.28697
81.722
0.27161
78.926
7i
o.35777
9I.45I
0.32553
89.168
O.29982
86.482
0.27970
83.518
0.26434
80.414
72
0.35176
94.122
0.31857
91.613
0.29226
88.655
0.27186
85.378
0.25649
81.932
73
0.34529
96.929
0.3 1 109
94.184
0.284I5
90.931
0.26343
87.310
0.24803
83.485
74
o.33 8 37
99.884
0.303 1 1
96.893
0.27548
93-325
0.25439
89.328
0.23894
85.081
75
0.33102
103.003
0.29464
99-757
0.26625
95-857
0.24475
91.448
0.22922
86.729
76
0.32328
106.302
0.28570
102.799
O.25648
98.547
0.23450
93690
0.21883
88.443
77
0.31519
109.799
0.27634
106.038
0.2462I
101.421
0.22366
96.078
0.20779
90.241
78
0.30680
113-513
0.26661
109.505
0.23546
104.512
0.21224
98.647
0.19610
92.146
79
0.29821
117.466
0.25659
113-231
0.2 243I
107.861
0.20030
101.437
0.18376
94.191
80
0.28950
121.678
0.24637
117.249
0.21284
m.519
0.18788
104.504
0.17082
96.419
81
0.28081
126.171
0.23609
121.599
0.20I l6
"5-543
0.17507
107.921
0.15730
98.893
82
0.27227
130.966
0.22589
126.322
O.I8943
120.004
0.16200
in. 784
0.14329
101.700
83
0.26405
136.078
0.21597
131-464
O.I7783
124.989
0.14880
116.221
0.12887
104.976
84
0.25633
141-517
0.20654
137.060
O.I6660
130.591
O.I3573
121.403
0.11419
108.916
85
0.24931
147.286
0.19786
143-143
O.I5604
136.907
0.12307
127.549
0.099443
113.839
86
0.24319
I53-370
0.19020
149.722
O.I465I
144.025
0.11122
134-931
0.084970
120.254
87
0.23818
159.740
0.18384
156.778
O.I3844
151.988
0.10074
I43.833
0.071310
128.990
88
0.23446
166.349
0.17906
164.253
O.I3224
160.762
0.092383
154456
0.059383
141.294
89
0.23216
173.129
0.17609
172.042
O.I2832
170.195
0.086890
166.709
0.050750
158.480
90
0.23138
180.000
0.17509
180.000
O.I2698
180.000
0.084969
180.000
0.047517
180.000
Note.
Negative quantities are in
heavy type.
Example
tanh (:
i-9 785)
/Q-O
= O.I2307
= 0.12307
\i27 u .549
\l27-32'-
56'.
2.9/85!
[31]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. / (p /45 ) = r /y
Sinh
Cosh
Tanh
0.
45.00
1.
0.
O.I
O.I OOOO
45.06
I.OOOOI
0.17
0.2
0.20000
45-23
I. 00013
1.09
-3
0.30001
45-52
1.0007
2-35
0.4
0.40005
46.32
1. 002 1
4-35
o-5
0.50016
47-23
1.0052
7.08
0.6
0.60042
48.27
1. 0107
10.15
0.7
0.70094
49.40
1.0198
J3-53
0.8
0.80184
51.06
1.0336
18.00
0.9
0.90327
52.44
1.0533
22.34
1.0
1-0055
54-32
1 .0803
27.29
1.1
1. 1089
56-31
1.1157
32-41
1.2
1-2138
58.41
1. 1608
38.05
i-3
1-3205
61.02
1. 2163
43-35
1.4
1.4297
63-34
1.2830
49-05
1-5
i-S4i8
66.15
1. 3616
54-33
1.6
1.6575
69.07
1.4524
59-55
i-7
1.7776
72.08
1.5556
65.09
1.8
1.9029
75.i8
1.6714
70.14
1.9
2.0343
78.36
1.7999
75-io
2.0
2.1726
82.01
1.9413
79-56
2.1
2.3190
85-34
2.0958
84.33
2.2
2-4745
89.12
2.2636
89.03
2-3
2.6404
92-57
2.4449
93.26
2.4
2.8177
96.46
2.6403
97-44
2.5
3.0079
100.39
2.8502
101.56
2.6
3.2121
104.36
3.0753
106.05
2.7
34318
108.36
3.3163
no. 10
2.8
3.6685
112.39
3.5741
114.15
2.9
3.9236
116.43
3.8497
118.16
3-o
4.1986
120.48
4.1443
122.16
3-i
4.4948
124.56
4.4589
126.15
3-2
4.8i54
129.02
4-7955
130.15
3-3
5.1586
133-09
5-I54I
134-13
3-4
5-53o6
137-17
5-5393
138.13
3-5
5.9305
141.24
5-9356
142.12
3.6
6.3603
145-31
6.3900
146. n
3-7
6.8244
149.38
6.8606
150.10
3-8
7.3228
153-44
7.3646
154.09
3-9
7.8590
I57-50
7.9047
158.10
4.0
8.4351
161.57
8.4831
162. n
4.1
9-0535
166.02
9.1024
166.12
4.2
9.7198
170.07
9.7704
170.13
4-3
10.434
174-11
10.481
174-15
4.4
11. 201
178.16
11.246
178.16
0.
45.00
0.09999
44-49
0.19997
44.14
0.29981
43-17
0.39921
41-57
0-49757
40.15
0.59406
38.11
0.68732
35-47
o.77577
33-o6
0.85756
30.10
0.93077
27.03
0.99389
23-50
1 -045 7
20.36
1.0857
17.27
1.1143
14.29
1. 1323
11.42
1.1413
9.12
1. 1428
6-59
1-1385
5 -04
1. 1302
3.26
1.1191
2.06
1. 1065
I.OI
1.0932
0.09
1.0799
0.29
1.0672
0.58
1 -0553
1. 17
1.0445
1.29
1.0348
1-34
1.0264
1.36
1.0192
1-33
1.0131
1.28
1.0080
1. 19
1. 004 1
1. 13
1.0008
1.04
0.9984
0.56
0.9967
0.48
0.9954
0.40
0-9947
0.32
0.9943
0.25
0.9942
0.20
o.9943
0.14
0.9946
O.IO
0.9948
0.06
0-9955
0.04
0.9960
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (1.7 /45 ) 1.7776 /72.o8'.
tanh (2.4/45!) " 1-0672 \o.58'.
[32]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. / (p /^) m r fa. Continued
Cosech
Sech
Coth
o.
00
45-00
I.
0.
00
45-00
O.I
10.0000
4506
0.99999
0.17
10.0000
44.49
0.2
5.0000
45-23
0.99987
1.09
5.0008
44.14
-3
3-3333
45-52
0.9993
2-35
3-3355
43-17
0.4
2.4997
46.32
0.9979
4-35
2.5050
41.57*
0.5
1.9984
47-23
0.9948
7.08
2.0096
40.15
0.6
1.6654
48.27
0.9894
10.15
1.6830
38.11
0.7
1.4268
49.40
0.9806
13-53
1-4549
35-47
0.8
1. 2471
5106
0.9675
18.00
1.2890
33o6
0.9
1. 1070
52.44
0.9494
22.34
1. 1660
30.10
1.0
0.9945
54-32
0.9256
27.29
1.0746
27.03
I.I
0.9018
56.31
0.8963
32.41
1. 006 1
23-50
1.2
0.8238
58.41
0.8614
38.05
0.9564
20.36
i-3
o.7573
61.02
0.8222
43-35
0.9211
17.27
1.4
0.6995
63-34
0.7793
49-05
0.8996
14.29
i-5
0.6486
66.15
o.7344
. 54-33
0.8831
11.42
1.6
0.6033
69.07
0.6885
59-55
0.8763
9.12
i-7
0.5625
72.08
0.6429
65.09
0.8751
6-59
1.8
0.5256
75-18
0.5981
70.14
0.8788
5-04
1.9
0.4916
78.36
0.5556
75-IO
0.8848
3-26
2.0
0.4603
82.01
0-5151
79-56
0.8936
2.06
2.1
0.4312
85.34
0.4772
84.33
0.9038
I.OI
2.2
0.4041
89.12
0.4418
89.03
0.9147
0.09
2-3
0.3788
92.57
0.4090
93-26
0.9260
0.29
2.4
o-3549
96.46
0.3788
97-44
0.9370
0.58
2-5
0.3325
100.39
0.3509
101.56
0.9476
1.17
2.6
0.31 14
104.36
0.3252
106.05
o.9574
1.29
2-7
0.2914
108.36
0.3016
no. 10
0.9663
1-34
2.8
0.2726
112.39
0.2798
114.15
0-9743
1.36
2.9
0.2549
116.43
0.2598
118.16
0.9812
i-33
3-
0.2382
120.48
0.2413
122.16
0.0871
1.28
3-i
0.2225
124.56
0.2243
126.15
0.9920
i.ig
3-2
0.2077
129.02
0.2085
130.15
0.9959
I-I3
3-3
0.1939
133-09
0.1940
134-13
0.9992
1.04
3-4
0.1808
137-17
0.1805
138.13
1.0016
0.56
3-5
0.1686
141.24
0.1681
142.12
1.0033
0.48
3-6
0.1572
145-31
0.1565
146. 1 1
1.0047
0.40
3-7
0.1465
149.38
0.1458
150.10
1-0053
0.32
3-8
0.1366
153-44
0.1358
154.09
1.0057
0.25
3-9
0.1272
I57-50
0.1265
158.10
1.0058
0.20
4.0
0.1 186
161.57
1 1 79
162. n
1.0057
0.14
4.1
0.1 105
166.02
0.1099
166.12
1.0054
0.10
4.2
0.1029
170.07
0.1024
170.13
1.0052
0.06
4-3
0.09584
174.11
0.09541
174-15
1.0045
0.04
4.4
0.08927
178.16
0.08892
178.16
1.0040
0.00
Note.
Negative quantities are in heavy type.
Examples, cosech (2.0 /45 ) = 0.4603 \82.oi'.
coth (2.5 /45 ) = 0.9476 /i-i7'-
[33]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. / (p /45 )
r fy. Continued
6.0
Sinh
34.784 243.05
Cosh
34.798 243.04
Tanh
4-5
12.026
182.19
12.067
182.19
0.9966
0.00
4.6
12.909
186.23
12.948
186.21
0.9970
0.02
4-7
13-858
190.27
13.894
190.23
0.9974
0.04
4.8
14.876
194.30
14.909
194.26
0.9978
0.04
4-9
15.968
I98-33
15-999
198.29
0.9980
0.04
S-o
17.140
202.36
17.169
202.32
0.9983
0.04
5-i
18.397
206.39
18.425
206.35
0.9985
0.04
5-2
19-747
210.42
19.772
210.38
0.9087
0.04
5-3
21.19S
214-45
21.219
214.41
0.9989
0.04
5-4
22.750
218.48
22.772
218.44
0.9990
0.04
5-5
24.418
222.50
24-439
222.47
0.9992
0.03
5-6
26.219
226.53
26.238
226.51
0.9993
0.02
5-7
28.141
230.56
28.159
230.54
0.9994
0.02
5-8
30.192
234-59
30.209
234-57
o.9995
0.02
5-9
32405
239.02
32.421
239.00
0.9996
0.02
0.9996
Cosech
6.0 0.02875 243.05
Sech
0.02874 243.04
Coth
4-5
0.08316
182.19
0.08288
182.19
1.0034
0.00
4.6
0.07746
186.23
0.07723
186.21
1.0030
0.02
4-7
0.07216
190.27
0.07197
190.23
1.0026
O.O4
4.8
0.06722
194.30
0.06707
194.26
1.0022
O.O4
4-9
0.06263
198.33
0.06250
198.29
1.0020
O.O4
5-o
0.05834
202.36
0.05824
202.32
1.0017
O.O4
5-i
0.05436
206.39
0.05428
206.35
1.0015
O.O4
5-2
0.05064
210.42
0.05058
210.38
1. 0013
O.O4
5-3
0.04718
214.45
0.04713
214.41
I.OOII
O.O4
5-4
0.04396
218.48
0.04391
218.44
I. OOIO
O.O4
5-5
0.04095
222.50
0.04092
222.47
1.0008
O.O3
5-6
0.03814
226.53
0.038 1 1
226.51
1.0007
0.02
5-7
0.03554
230.56
0-03551
230.54
1.0006
0.02
5-8
0.03312
234-59
0.03310
234-57
1.0005
0.02
5-9
0.03086
239.02
0.03085
239.00
1.0004
0.02
1.0004 ' 01
Note.
Negative quantities are in heavy type.
Examples, tanh (6.0 /45 ) = 0.9996 /o.oi'.
sech (5.0 /45 ) = 0.05824 \202.32'.
[34]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. /(p/45 ) - r /y. Continued
p Sinh and cosh Tanh and coth Sech and cosech
O / O o /
6.05 36.047 245.06 1. 000 0.00 2.774X10- 2 245.06
6.10 37-349 247.08 1.000 0.00 2.678 " 247.08
6.15 38-693 249.09 1.000 0.00 2.583 ' 249.09
6.20 40.084 251. 11 1.000 0.00 2.495 " 251. 11
6.25 41-524 253.12 1.000 0.00 2.408 " 253.12
6.30 43-020 255.14 1.000 0.00 2.325 " 255.14
6.35 44-563 257.15 1.000 0.00 2.244 " 257.15
6.40 46.171 259.17 1.000 0.00 2.166 " 259.17
6.45 47-832 261.18 1.000 0.00 2.091 " 261.18
6.50 49-553 263.20 1.000 0.00 2.018 " 263.20
6 -55 5J-33 6 265.22 1.000 0.00 1.948 " 265.22
6.60 53-183 267.24 1.000 0.00 1.880 u 267.24
6.65 55- XI 269.25 1.000 0.00 1.815 " 269.25
6.70 57-058 271.27 1.000 0.00 1.752 " 271.27
6.75 59-136 273.28 1.000 0.00 1.691 " 273.28
6.80 61.259 275.30 1.000 0.00 1.632 " 275.30
6.85 63.463 277.31 1.000 0.00 1.576 " 277.31
6.90 65.746 279.33 I - 0.00 1. 521 * 279.33
6.95 68.119 281.34 1.000 0.00 1.468 " 281.34
7.00 7-57 283.36 1.000 0.00 1.417 " 283.36
7.05 73- io 9 285.37 1. 000 0.00 1.368 " 285.37
7.10 75-739 287.39 1.000 0.00 1.312 " 287.39
7.15 78.473 289.40 1.000 0.00 1-274 " 289.40
7.20 81.296 291.42 1.000 0.00 1.230 " 291.42
7.25 84.215 293.43 1.000 0.00 1. 187 " 293.43
7.30 87.250 295.45 1.000 0.00 1. 146 " 295.45
7.35 90.386 297.46 1. 000 0.00 1. 016 " 297.46
7.40 93-083 299.48 1.000 0.00 1-074 " 299.48
7.45 97.009 301.49 1.000 0.00 1.031 " 301.49
7.50 100.50 303.51 1. 000 0.00 9.95oXio~ 3 303.51
7.55 104.12 305-52 i-ooo 0.00 9.605 305-52
7.60 107.86 307.54 1.000 0.00 9.271 " 307-54
7.65 1 1 1.74 309.56 1. 000 0.00 8.949 " 309.56
7.70 115-67 3U-57 1.000 0.00 8.638 " 311.57
7.75 H9-94 3 I 3-59 i-ooo 0.00 8.337 " 313-50
7.80 124.26 316.00 1.000 0.00 8.048 " 316.00
7.85 128.71 318.02 1.000 0.00 7.769 " 318.02
7.90 133-35 320.03 1.000 0.00 7.499 ' 320.03
7.95 138.16 322.05 1.000 0.00 7.238 " 322.05
8.00 143.12 324.06 1.000 0.00 6.987 " 324.06
8.05 148.28 326.07 1.000 0.00 6.744 " 326.07
8.10 153-61 328.09 1.000 0.00 6.510 " 328.09
8.15 159-14 330.11 1.000 0.00 6.284 " 330.11
8.20 164.87 332.12 1.000 0.00 6.066 " 332.12
8.25 170.80 334.14 i-ooo 0.00 5-855 " 334-14
Note. Negative quantities are in heavy type.
Examples, sinh (7.55 /45 ) = cosh (7.55 /45 ) = 104.12 /3Q5-52 / .
sech (7-50 /45 ) = cosech (7-50 /45 ) = 9-95 X 10 3 \303.5i'-
[35]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. / (p /45 ) = r /y. Continued
p
Sinh and cosh
Tanh and coth
Sech and cosech
8.30
176.95
336.15
1. 000
0.00
5.651 Xio~ 3
336.15
8-35
183.31
338.17
1. 000
0.00
5-455 "
338.17
8.40
189.91
340.18
1. 000
0.00
5.266 "
340.18
8.45
I96-75
342.20
1. 000
0.00
5-o8 3 "
342.20
8.50
203.83
344.22
1. 000
0.00
4.906 "
344-22
8-55
211. 16
346.24
1. 000
0.00
4-736 "
346.24
8.60
218.76
348.25
1. 000
0.00
4-571 "
348.25
8.6 S
226.63
350.27
1. 000
0.00
4-4I3 "
350.27
8.70
234-79
352.28
1. 000
0.00
4-259 '
352.28
8-75
243-23
354-30
1. 000
0.00
4. 1 1 1 "
354-30
8.80
25L99
356.31
1. 000
0.00
3-968 "
356.31
8.8 S
261.06
358.33
1. 000
0.00
3-830 "
358.33
8.90
270.46
360.34
1. 000
0.00
3.698 '
360.34
8-95
280.19
362.36
1. 000
0.00
3-569
362.36
9.00
290.28
364.38
1. 000
0.00
3-445
364.38
9-5
300.73
366.39
1. 000
0.00
3-3253 "
366.39
9.10
3"-54
368.41
1. 000
0.00
3.2099 '
368.41
9-i5
322.7S
370.42
1. 000
0.00
3-0983
370.42
9.20
334-37
372.44
1. 000
0.00
2.9908 "
372.44
9-25
346.39
37446
1. 000
0.00
2.8869 "
374-46
9-3
358.85
376.47
1. 000
0.00
2.7867 "
376.47
9-35
37i.8i
378.48
1. 000
0.00
2.6895 "
378.48
9.40
385-I5
380.50
1. 000
0.00
2.5964 '
380.50
9-45
399.04
382.51
1. 000
0.00
2.5060 "
382.51
9-5
413-38
384.53
1. 000
0.00
2.4191 "
384-53
9-55
428.26
386.55
1. 000
0.00
2-335 "
386.55
9.60
443-67
388.56
1. 000
0.00
2.2540 '
388.56
9-65
446.93
390.57
1. 000
0.00
2.2263 "
390.57
9.70
476.18
392.59
1. 000
0.00
2.1001 "
39259
9-75
493 -3 1
395 -o 1
1. 000
0.00
2.0271 "
395-01
9.80
511.07
397.02
1. 000
0.00
1-9567 "
397.02
9-85
529.46
39903
1. 000
0.00
1.8887 '
399-03
9.90
548.52
401.05
1. 000
0.00
1.8231 "
401.05
9-95
568.25
403.07
1. 000
0.00
I.7598 '
403.07
10.00
588.69
405.08
1. 000
0.00
1.6987 "
405.08
10.05
609.89
407.09
1. 000
0.00
1.6397 "
407.09
10.10
631.84
409.11
1. 000
0.00
1.5827 *
409.11
10.15
654.58
411. 13
1. 000
0.00
I.5277 "
411. 13
10.20
678.14
413-14
1. 000
0.00
1.4746 "
4I3-I4
10.25
702.53
415-15
1. 000
0.00
1.4234 "
4I5-I5
10.30
727.81
417.17
1. 000
0.00
I-3740 "
417.17
IO -35
754-OI
419.19
1. 000
0.00
1.3262 '
419.19
10.40
781.14
421.21
1. 000
0.00
1.2802 "
421.21
10.45
809.26
423-23
1. 000
0.00
1.2357 "
42323
10.50
838.38
425-24
1. 000
0.00
1. 1928 "
425.24
Note. Negative quantities are in heavy type.
Examples.
sinh (10.0 /4s ) = cosh (10.0 [45) = 588.69 /4os.o8'.
sech (10.0 / 4 s) = cosech (10.0 /45 ) = 1.6987 X io" 3 \405.o8' = 1.6987 X io" 3 \45.o8'.
[36]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. /(p/45) -*/% Continued
p
Sinh and cosh
Tanh and coth
Sech and cosech
10.55
868.56
427.26
1. 000
0.00
1.1513X10- 3
427.26
10.60
899.81
429.27
1. 000
0.00
1.1113
429.27
10.65
932.18
43^29
1. 000
0.00
1.0728
u
431-29
10.70
965-74
433-30
1. 000
0.00
1-0555
u
43330
io.75
1,000.5
435-32
1. 000
0.00
9.9952 X TO 4
435.32
10.80
1,036.5
437-33
1. 000
0.00
9.6478
a
437-33
10.85
1,073.8
439-35
1. 000
0.00
9.3128
"
439-35
10.90
1,112.4
441.36
1. 000
0.00
8.9892
u
441.36
10.95
1,152.5
443-38
1. 000
0.00
8.6770
a
443-38
11.00
1,194.0
445-39
1. 000
0.00
8.3750
445-39
11.05
1,237-0
447.41
1. 000
0.00
8.0845
a
447.41
11. 10
1,281.5
449.42
1. 000
0.00
7.8037
449.42
11.15
i,327-5
451-44
1. 000
0.00
7-5327
u
451-44
11.20
i,375-3
453-46
1. 000
0.00
7.2711
u
453-46
11.25
1,424.8
455-47
1. 000
0.00
7.0184
U
455-47
11.30
1,476.1
457-48
1. 000
0.00
6.7747
457-48
"35
1,529.2
459-50
1. 000
0.00
6.5393
a
459-50
11.40
1,584-3
561.52
1. 000
0.00
6.3120
u
461.52
"45
1,641.4
463-53
1. 000
0.00
6.0929
a
463.53
11.50
1,700.3
465-54
1. 000
0.00
5.8811
u
465-54
"55
1,761.5
467.56
1. 000
0.00
5.6769
a
467.56
11.60
1,824.9
469-57
1. 000
0.00
5-4797
a
469-57
11.65
1,890.6
471-59
1. 000
0.00
5-2893
u
471-59
11.70
1,958.6
474.01
1. 000
0.00
5-1056
u
474.01
"75
2,029.1
476.03
1. 000
0.00
4.9282
u
476.03
11.80
2,102.1
478.04
1. 000
0.00
4-7571
u
478.04
11.8s
2,177.8
480.05
1. 000
0.00
4.5910
u
480.05
11.90
2,256.1
482.07
1. 000
0.00
4-4323
it
482.07
"95
2,337-3
484.09
1. 000
0.00
4.2784
flf
484.09
12.00
2,421.5
486.10
1. 000
0.00
4.1297
486.10
12.05
2,508.6
488.12
1. 000
0.00
3.9862
u
488.12
12.10
2,598.9
490.14
1. 000
0.00
3.8478
490.14
12.15
2,692.6
492.15
1. 000
0.00
3-7i4i
492.15
12.20
2,789.0
494.17
1. 000
0.00
3-5856
a
494.17
12.25
2,889.7
496.18
1. 000
0.00
3-4605
496.18
12.30
2,993-7
498.20
1. 000
0.00
3-3403
a
498.20
12.35
3,101.4
500.21
1. 000
0.00
3-2243
500.21
12.40
3,213-1
502.23
1. 000
0.00
3-oi43
502.23
12.45
3,328.3
504.24
1. 000
0.00
3.0042
"
504-24
12.50
3,448.5
506.26
1. 000
0.00
2.8998
u
506.26
12.55
3,572.6
508.27
1. 000
0.00
2.7991
u
508.27
12.60
3,7oi.i
510.29
1. 000
0.00
2.7019
"
510.29
12.65
3,834.3
512.31
1. 000
0.00
2.6080
u
512.31
12.70
3,972.6
5I4.32
1. 000
0.00
2.5172
5I4-32
12.75
4,"5-3
516.33
1.000
0.00
2.4300
516.33
Note. Negative quantities are in heavy type.
Examples, sinh (12.0 /45 ) = cosh (12.0 J_^) = 2421.5 /486 .IO , = 2421.5 /i26.io'.
sech (12.75/45!) " cosech ( I2 -75/4S!) = 2.43 X io- 3 \5i6.33'-
[37]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. /(p/45 ) = r /y. Continued
p
Sinh and cosh
Tanh and coth
Sech and cosech
12.80
4,263.4
518.35
1.000
0.00
2.3455X
10 4 518.35
12.85
4,416.8
520.37
1. 000
0.00
2.2641
520.37
12.90
4,575-7
522.38
1. 000
0.00
2.1854
522.38
12.95
4,74o.5
524-39
1. 000
0.00
2.1095
524-30
13.00
4,911.0
526.41
1. 000
0.00
2.0362
" 526.41
13-05
5,087.8
528.43
1. 000
0.00
1-9655
528.43
13.10
5,270.9
53-44
1. 000
0.00
1.8972
430.44
13-15
5,460.6
532.45
1. 000
0.00
1-8313
532.45
13.20
5,657-o
534-47
1. 000
0.00
1.7677
534-47
13-25
5,858.5
536.49
1. 000
0.00
1. 7061
536.49
13-30
6,071.6
538.50
1. 000
0.00
1.6470
538.50
13-35
6,290.1
540.5I
1. 000
0.00
1.5898
540.51
13.40
6,516.5
542.53
I.OOO
0.00
1-5346
542.53
13-45
6,751.0
544-55
1. 000
0.00
1.4813
544-55
I3-50
6,993-9
546.57
1.000
0.00
1.4298
546.57
13-55
7,245-5
548.58
1.000
0.00
1. 3801
548.58
13.60
7,506.4
55i-oo
1.000
0.00
1.3322
551-00
13-65
7,776.4
553-oi
1.000
0.00
1.2859
553-01
13.70
8,056.4
555-03
1.000
0.00
1. 2412
555-03
13-75
8,346.2
557-oS
1.000
0.00
1. 1982
557-05
13.80
8,646.7
559-o6
1.000
0.00
1-1565
559-06
13-85
8,957-8
561.07
1.000
0.00
I.I 164
561.07
13.90
9,280.3
563-09
1.000
0.00
1.0776
56309
13-95
9,614.1
565-11
1.000
0.00
1.0165
565-11
14.00
9,960.2
567.12
1.000
0.00
1.0040
567.12
14.05
10,318
569.14
1.000
0.00
9.6914X
to -5 569.14
14.10
10,690
57i-i5
1.000
0.00
9-3547
571-15
14-15
n,o75
573-i6
1.000
0.00
9.0296 '
573-i6
14.20
n,473
575-i8
1.000
0.00
8.7160 '
575-i8
14-25
11,886
577.20
1.000
0.00
8.4132 '
577-20
14.30
12,314
579-21
1.000
0.00
8.1210 '
579-21
14-35
12,757
581.22
1.000
0.00
7.8388 '
581.22
14.40
13,216
583-24
1.000
0.00
7.5666 '
583-24
14-45
13,692
585.26
1.000
0.00
7.3037 '
' 585.26
14.50
14,184
587-27
1.000
0.00
7.0500 '
587.27
14-55
14,695
589.29
1.000
0.00
6.8050 '
289.29
14.60
15,224
59I-30
1.000
0.00
6.5687 '
59I-30
14.65
15,772
593-32
1.000
0.00
6.3405 '
593-32
14.70
16,339
595-34
1.000
0.00
6.1203 '
595-34
14-75
16,927
597-35
1.000
0.00
5.9077 '
597-35
14.80
17,536
599-37
1.000
0.00
5-7024 '
599-37
14.85
18,167
601.39
1.000
0.00
5.5044 '
601.39
14.90
18,822
603.40
1.000
0.00
5.3I30 *
603.40
14-95
19,498
605.41
1.000
0.00
5.1286 '
605.41
15.00
20,200
607.43
1.000
0.00
4.9504 '
607.43
Note. Negative quantities are in heavy type.
Examples, sinh (14.0 /45 ) = cosh (14.0 745) = 9960.2 /567.i2'
sech (14.0 /45) cosech (14.0 /45 ) = 1.0040 X io~ 4 \s67.i2'.
[38]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. f (p [if) = r [y. Continued
p
Sinh and cosh
/
Tanh and coth
Sech and cosech
15.05
20,927
609.44
1. 000
0.00
4.7785 Xio-s
609.44
15-10
21,680
611.46
1. 000
0.00
4.6120
u
611.46
15-15
22,460
613.48
1. 000
0.00
44523
u
613.48
15.20
23,269
615.49
1. 000
0.00
4.2980
u
6I5.49
15-25
24,106
617.50
1. 000
0.00
4.1482
u
617.50
15-30
24,973
619.52
1. 000
0.00
4.0040
u
619.52
15-35
25,873
621.54
1.000
0.00
3-8651
u
621.54
15.40
26,802
623.55
1. 000
0.00
3-73IO
a
623.55
15-45
27,768
625.57
1. 000
0.00
3.6012
u
625.57
15.50
28,765
627.59
1. 000
0.00
3.4760
627.59
15-55
29,803
630.00
1. 000
0.00
3-3554
63O.OO
15.60
30,872
632.02
1. 000
0.00
3-2390
u
632.02
15-65
31,987
634.04
1. 000
0.00
3.1263
u
634.04
i5-7o
33,Mo
636.05
1. 000
0.00
3.0170
u
636.05
15-75
34,33i
638.06
1. 000
0.00
2.9129
u
638.06
15-80
35,569
640.08
1. 000
0.00
2.8110
a
640.08
15.85
36,846
642.10
1. 000
0.00
2.7140
a
642.IO
15.90
38,174
644.11
1. 000
0.00
2.6200
a
644.II
15-95
39,546
646.12
1. 000
0.00
2.5287
u
646.12
16.00
40,970
648.14
1. 000
0.00
2.4410
u
648.14
16.05
42,443
650.16
1. 000
0.00
2.3561
a
650.16
16.10
43,97i
652.17
1. 000
0.00
2.2740
a
652.17
16.15
45,553
654.18
1. 000
0.00
2.1952
u
654.18
16.20
47,192
656.20
1. 000
0.00
2.1 190
u
656.20
16.25
48,890
658.22
1. 000
0.00
2.0454
u
658.22
16.30
50,649
660.23
1. 000
0.00
1.9740
u
660.23
16.35
52,473
662.24
1. 000
0.00
I-9055
u
662.24
16.40
54,359
664.26
1. 000
0.00
1.8400
664.26
16.45
56,316
666.28
1. 000
0.00
1-7757
666.28
16.50
58,475
668.29
1. 000
0.00
1. 7100
a
668.29
16.55
60,444
670.31
1. 000
0.00
1.6544
u
670.31
16.60
62,619
672.32
1. 000
0.00
1.5969
a
672.32
16.65
64,872
674-34
1. 000
0.00
I-54I5
u
674-34
16.70
57,2o8
676.35
1. 000
0.00
1.4879
a
676.35
16.75
69,626
678.36
1. 000
0.00
1.4362
a
678.36
16.80
72,132
680.38
1. 000
0.00
1.3863
u
680.38
16.85
74,727
682.40
1. 000
0.00
1.3382
a
682.40
16.90
77,4i8
684.41
1. 000
0.00
1. 2917
a
684.41
16.95
80,203
686.43
1. 000
0.00
1.2468
a
686.43
17.00
83,088
688.45
1. 000
0.00
1-2035
a
688.45
17-05
86,080
690.47
1. 000
0.00
1.16x7
u
690.47
17.10
89,176
692.48
1. 000
0.00
1.1214
a
692.48
17-15
92,387
694.49
1. 000
0.00
1.0824
u
694.49
17.20
95,7n
696.51
1. 000
0.00
1.0448
u
696.51
17-25
99,149
698.53
1. 000
0.00
1.0086
u
698.53
Note. Negative quantities are in heavy type.
Examples, sinh (17.0 /45I) = cosh (17.0/45) = 83,088 /688. 4 5 / = 83,088 /328. 4 5'-
sech (17.0 /45 ) = cosech (17.0 /45 ) = 1.2035 X io~ B \688.4s'.
[39]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. / (p /45 ) = r Ay. Continued
p
Sinh and cosh
/
Tanh and coth
Sech and cosech
17.30
102,720
700.54
1. 000
0.00
9.7349X10- 6
700.54
17-35
106,420
702.55
1. 000
0.00
9.3968
702.5s
17.40
110,250
704-57
1. 000
0.00
9.0703
u
704-57
1745
114,220
706.59
1. 000
0.00
8.7551
a
706.59
17-5
118,330
709.00
1. 000
0.00
8.4510
u
709.00
17-55
122,590
711.01
1. 000
0.00
8.1576
u
711.01
17.60
127,000
713-03
1. 000
0.00
7.8741
a
713.03
17-65
i3i,57o
7i5-o5
1. 000
0.00
7.6006
a
715.05
17.70
136,300
717.06
1. 000
0.00
7-3365
u
717.06
17-75
141,210
719.07
1. 000
0.00
7.0817
u
719.07
17.80
146,290
721.09
1.000
0.00
6.8356
a
721.09
17.85
151,550
723.11
1. 000
0.00
6.5983
u
723.11
17.90
157,000
725.12
1. 000
0.00
6.3710
u
725.12
17-95
162,660
727.13
1. 000
0.00
6.1478
a
727.13
18.00
168,520
729.15
1. 000
0.00
5-9383
729.15
18.05
i74,58o
l^-^l
1. 000
0.00
5.7281
731.17
18.10
180,860
733-i8
1. 000
0.00
5-5292
733.18
18.15
183,530
735-2Q
1. 000
0.00
5-4488
a
735-20
18.20
194,110
737-21
1. 000
0.00
5-I5I7
737-21
18.25
201,100
739-23
1. 000
0.00
4.9727
u
739-23
18.30
208,330
741.24
1. 000
0.00
4.8000
a
741.24
i8-35
215,830
743.26
1. 000
0.00
4-6332
u
743.26
18.40
223,600
745-27
1. 000
0.00
44723
u
745-27
18.45
231,650
747.29
1. 000
0.00
4.3168
747.29
18.50
239,980
749-31
1. 000
0.00
4.1671
749-31
18.55
248,620
75I-32
1. 000
0.00
4.0222
u
751-32
18.60
257,570
753-34
1. 000
0.00
3-8825
753-34
18.65
266,840
755-35
1. 000
0.00
3-7476
u
755-35
18.70
276,440
757-37
1. 000
0.00
3-6i74
u
757-37
18.75
286,390
759-38
1. 000
0.00
3.4918
759.38
18.80
296,690
761.40
1. 000
0.00
3.3628
a
761.40
18.85
307,380
763-41
1.000
0.00
3-2533
u
76341
18.90
318,570
76543
1. 000
0.00
3.1404
u
76543
18.95
329,890
767.44
1. 000
0.00
3-0313
u
767.44
19.00
34i,77o
769.46
1. 000
0.00
2.9260
u
769.46
19.05
354,o6o
771-47
1. 000
0.00
2.8244
u
771-47
19.10
366.810
773-49
1. 000
0.00
2.7262
a
77349
I9-I5
380,010
775-50
1. 000
0.00
2.6315
a
775-50
19.20
393,690
777-52
1.000
0.00
2.5401
a
777-52
19-25
407,850
779-53
1. 000
0.00
2.4519
779-53
19.30
422,530
78i.55
1. 000
0.00
2.3667
78i.55
19-35
437,730
783-57
1. 000
0.00
2.2845
u
783-57
19.40
453,490
785-59
1. 000
0.00
2.2051
u
785-59
19-45
469,810
788.00
1. 000
0.00
2.1285
u
788.00
19.50
486,720
790.02
1. 000
0.00
2.0546
u
790.02
Note. Negative qyantities are in
heavy type.
Examples, sinh (19.05 745
) = cosh (
r 9-05 A45
!) = 354
,060/771-
47' =
354,o6o
sech (19.30 /45 ) = cosech (19.3 /45 ) = 2.3667 X io-\78i .55'.
[40]
Table VI
FUNCTIONS OF SEMI-IMAGINARIES. /(p/45 ) m'r/y. Continued
p
Sinh and cosh
Tanh and coth
Sech and cosech
19-55
504,230
792.03
1. 000
0.00
1.9832 Xio -6
792.03
19.60
522,380
794-05
1. 000
0.00
i-9i53
794-05
19.65
541,220
796.06
1. 000
0.00
1.8478
796.06
19.70
560,650
798.08
1. 000
0.00
1-7837
u
798.08
19-75
599,830
800.09
1. 000
0.00
1.6671
u
800.09
19.80
601,730
802.11
1. 000
0.00
1.6619
802.11
19.85
623,390
804. 1 2
1. 000
0.00
1. 6041
804.12
19.90
645,820
806.14
1. 000
0.00
1.5484
806.14
19-95
669,070
808.15
1.000
0.00
1.4946
a
808.15
20.00
693, I 5
810.17
1. 000
0.00
1.4426
810.17
20.05
7l8,090
812.18
1. 000
0.00
1.3926
a
812.18
20.10
743,930
814.20
1. 000
0.00
1-3442
"
814.20
20.15
770,710
816.21
1. 000
0.00
1-2975
u
816.21
20.20
798,440
818.23
1. 000
0.00
1.2525
((
818.23
20.25
827,l6o
820.24
1. 000
0.00
1.2090
u
820.24
20.30
856,940
822.26
1. 000
0.00
1. 1669
a
822.26
20.35
887,770
824.27
1. 000
0.00
1. 1264
a
824.27
20.40
9 J 9,730
826.29
1. 000
0.00
1.0873
a
826.29
20.45
952,820
828.30
1. 000
0.00
1 .0496
u
828.30
20.50
987,120
830.32
1. 000
0.00
1. 0130
a
830.32
Note. Negative quantities are in heavy type.
Example, sinh (20.0 /45 ) = cosh (20.0 /45 ) - 693,150/810^17/ = 693,150/90^11^
[41]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv
x 0.05
x = 0.15
0.0
0.00
0.00
0.05002
0.00
0.10017
0.00
0.15056
0.00
0.20134
0.00
0.0s
0.00
0.07846
0.04987
0.07856
0.09986
0.07885
0.15010
0.07934
0.20072
0.08003
O.I
0.00
0.15643
0.04945
0.15663
0.09893
0.15722
0.14871
0.15820
0.19886
0.15957
0.15
0.00
c-23345
0.04864
0.23374
0.09740
0.23461
0.14640
0.23608
0.19577
0.23813
0.2
0.00
0.30902
0.04757
0.30940
0.09526
0.31056
0.143 19
0.31250
0.19148
0.31522
0.25
0.00
0.38268
0.04621
c.38316
0.09254
0.38460
0.13910
0.38700
0.1 8601
0.39036
o-3
0.00
c-45399
0.04457
o.45454
0.08925
0.45626
0.13415
0.4591 I
0.17939
0.46310
o-3S
0.00
0.52250
0.04265
0.52313
0.08541
0.52511
0.12838
0.52839
0.17167
0.53298
0.4
0.00
0.58778
0.04047
0.58850
0.08104
0.59073
0.12181
0.59441
c.16288
0.59958
0.4s
0.00
0.64944
0.03804
0.65023
0.07617
0.65270
0.1 1449
0.65677
0.15310
0.66248
-5
0.00
0.70711
0.03537
0.70796
0.07083
0.71065
0.10646
0.71508
0.14237
0.72130
o-55
0.00
0.76041
0.03249
0.76133
0.06505
0.76421
0.09778
0.76898
0.13076
0.77567
0.6
0.00
0.80902
0.02940
0.81000
0.05888
0.81307
0.08850
0.81814
0.1 1834
0.82525
0.65
0.00
0.85264
0.02614
0.85367
0.05234
0.85691
0.07867
0.86225
0.10520
0.86975
0.7
0.00
0.89101
0.02271
0.89208
0.04547
0.89547
0.06835
0.90105
0.09 141
0.90889
0-7S
0.00
0.92388
0.01914
0.92503
0.03833
0.92850
0.05762
0.93429
0.07705
0.94242
0.8
0.00
0.95106
0.01546
0.95225
0.03095
0.95582
0.04653
0.96178
0.06222
0.97014
0.85
0.00
0.97237
0.01168
0-97359
0.02338
0.97724
0.03515
0.98333
0.04700
0.99188
0.9
0.00
0.98769
0.00783
0.98892
0.01567
0.99263
0.02355
0.99882
0.03150
1.00751
o.95
0.00
0.99692
0.00392
0.99816
0.00786
1.00191
0.01181
1.00815
0.01580
]. 01692
1.0
0.00
1. 00000
0.00
1.00125
0.00
1.00500
0.00
1.01127
0.00
1.02007
1.05
0.00
0.99692
0.00392
0.99816
0.00786
1.00191
0.01181
1. 008 1 5
0.01580
1. 01692
1.1
0.00
0.98769
0.00783
0.98892
0.01567
0.99263
0.02355
0.99882
0.03150
1. 0075 1
i-i5
0.00
0.97237
0.01168
o.97359
0.02338
0.97724
0.03515
0-98333
0.04700
0.99188
1.2
0.00
0.95106
0.01546
0.95225
0.03095
0.95582
0.04653
0.96178
0.06222
0.97014
1. 25
0.00
0.92388
0.01914
0.92503
0.03833
0.92850
0.05762
0.93429
0.07705
0.94242
i-3
0.00
0.89101
0.02271
0.89208
0.04547
0.89547
0.06835
0.90105
0.09141
0.90889
i-35
0.00
0.85264
0.02614
0.85367
0.05234
0.85691
0.07867
0.86225
0.10520
0.86975
1.4
0.00
0.80902
0.02940
0.81000
0.05888
0.81307
0.08850
0.81814
0.11834
0.82525
1-45
0.00
0.76041
0.03249
0.76133
0.06505
0.76421
0.09778
0.76898
0.13076
0.77567
i-5
0.00
0.70711
0.03537
0.70796
0.07083
0.71065
0.10646
0.71508
0.14237
0.72130
1-55
0.00
0.64944
0.03804
0.65023
0.07617
0.65270
0.1 1449
0.65677
0.15310
0.66248
1.6
0.00
0.58778
0.04047
0.58850
0.08104
0.59073
0.12181
0.59441
0.16288
0.59958
1.65
0.00
0.52250
0.04265
0.52313
0.08541
0.52511
0.12838
0.52839
0.17167
0.53298
i-7
0.00
0-45399
0.04457
0-45454
0.08925
0.45626
0.13415
0.4591 1
0.17939
0.46310
1-75
0.00
0.38268
0.04621
0.38316
0.09254
0.38460
0.13910
0.38700
0.18601
0.39036
1.80
0.00
0.30902
0.04757
0.30940
0.09526
0.31056
0.14319
0.31250
0.19148
0.31522
i.8 S
0.00
0.23345
0.04864
0.23374
0.09740
0.23461
0.14640
0.23608
0.19577
0.23813
1.9
0.00
0.15643
0.04945
0.15663
0.09893
0.15722
0.14871
0.15820
0.19886
0.15957
1 -95
0.00
0.07845
0.04987
0.07856
0.09986
0.07885
0.15010
0.07934
0.20072
0.08003
2.0
0.00
0.00
0.05002
0.00
0.10017
0.00
0.15056
0.00
0.20134
0.00
Note.
Negative
quantities are in heavy type.
Examples.
sinh (0.1
+ i Q-5) '
= 0.07083 + i 0.710!
>5-
sinh (0.1 + i 1.2) m 0.03095 + * 0.95582.
[42]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
x = 0.25
x - 0.3
* - o-35
x = 0.4
x = 0.45
0.25261
0.00
0.30452
0.00
o.357i9
0.00
0.41075
0.00
0.46534
0.00
0.05
0.25183
0.08092
0.30358
0.08202
0.35609
0.08331
0.40949
0.08482
0.46391
0.08654
O.I
0.24950
0.16135
0.30077
0.16353
0.35279
0.16611
0.40570
0.16912
0.45961
0.17254
0.15
0.24563
0.24078
0.29611
0.24403
o.34732
0.24789
0.39940
0.25237
0.45249
0.25748
0.2
0.24025
0.31872
0.28962
0.32303
o.3397i
0.32814
0.39065
0.33407
0.44257
0.34084
0.25
0.23338
0.39471
0.28134
0.40003
0.33000
0.40636
o.37949
0.41371
0.42992
0.42209
o-3
0.22508
0.46825
0.27133
o.47457
0.31826
0.48208
0.36598
0.49080
0.41462
0.50074
o-3S
0.21539
0.53891
0.25965
0.54619
0.30455
0.55483
0.35022
0.56486
0.39677
0.57630
0.4
0.20437
0.60625
0.24636
0.61444
0.28897
0.62416
0.33231
0.63544
0.37647
0.64831
o.45
0.19208
0.66985
0.23156
0.67889
0.27161
0.68964
0.31234
0.70210
0.35385
0.71632
0.5
0.17862
0.72932
0.21533
0.73917
0.25257
0.75086
0.29045
0.76443
0.32905
0.77992
o-55
0.16406
0.78429
0.19777
0.79488
0.23198
0.80746
0.26676
0.82206
0.30222
0.83871
0.6
0.14848
0.83443
0.17899
0.84570
0.20995
0.85908
0.24143
0.87461
0.27352
0.89232
0.65
0.13199
0.87942
0.15911
0.89130
0.18663
0.90540
0.21462
0.92177
0.24314
0.94044
0.7
0.1 1468
0.91900
0.13825
0.93140
0.16216
0.94614
0.18648
0.96324
0.21126
0.98275
o.7S
0.09667
0.95290
0.11654
0.96577
0.13669
0.98105
0.15719
0.99878
0.17808
1.01901
0.8
0.07801
0.98093
0.09410
0.99418
0.1 1038
1. 0099 1
0.12693
1.02816
0.14380
1 .04899
0.85
0.05897
1.00292
0.07109
1.01646
0.08338
1-03254
0.09589
1. 05 1 20
0.10863
1.07250
0.9
0.03952
1.01871
0.04764
1.03247
0.05588
1 .04880
0.06426
1.06776
0.07280
1.08939
o-95
.0.01982
1.02823
0.02389
1. 042 1 2
0.02803
1.05860
0.03223
1.07774
0.03651
1.09957
1.0
0.00
1. 03 141
0.00
1.04534
0.00
1. 06 1 88
0.00
1.08107
0.00
1. 10297
1.05
0.01982
1.02823
0.02389
1.042 1 2
0.02803
1.05860
0.03223
1.07774
0.03651
1.09957
1.1
0.03952
1.01871
0.04764
1.03247
0.05588
1 .04880
0.06426
1.06776
0.07280
1.08939
i-i5
0.05897
1.00292
0.07109
1.01646
0.08338
1.03254
0.09589
1. 05 1 20
0.10863
1.07250
1.2
0.07801
0.98093
0.09410
0.99418
0.11038
1. 0099 1
0.12693
1.02816
0.14380
1 .04899
1-25
0.09667
0.95290
0.11654
0.96577
0.13669
0.98105
0.15719
0.99878
0.17808
1.01901
i-3
0.11468
0.91900
0.13825
0.93140
0.16216
0.94614
0.18648
0.96324
0.21126
0.98275
i-35
0.13199
0.87942
0.15911
0.89130
0.18663
0.90540
0.21462
0.92177
0.24314
0.94044
1.4
0.14848
0.83443
0.17899
0.84570
0.20995
0.85908
0.24143
0.87461
0.27352
0.89232
i-4S
0.16406
0.78429
0.19777
0.79488
0.23198
0.80746
0.26676
0.82206
0.30222
0.83871
i-5
0.17862
0.72932
0.21533
0.73917
0.25257
0.75086
0.29045
0.76443
0.32905
o.77992
i-55
0.19208
0.66985
0.23156
0.67889
0.27161
0.68964
0.31234
0.70210
0.35385
0.71632
1.6
0.20437
0.60625
0.24636
0.61444
0.28897
0.62416
0.33231
0.63544
0.37647
0.64831
1. 65
0.21539
0.53891
0.25965
0.54619
0.3045S
0.55483
0.35022
0.56486
0.39677
0.57630
i-7
0.22508
0.46825
0.27133
o.47457
0.31826
0.48208
0.36598
0.49080
0.41462
0.50074
i-7S
0.23338
0.39471
0.28134
0.40003
0.33000
0.40636
o.37949
0.41371
0.42992
0.42209
1.8
0.24025
0.31872
0.28962
0.32303
0.33971
0.32814
0.39065
0.33407
0.44257
0.34084
1.85
0.24563
0.24078
0.29611
0.24403
o.34732
0.24789
0.39940
0.25237
0.45249
0.25748
1.9
0.24950
0.16135
0.30077
0.16353
0.35279
0.16611
0.40570
0.16912
0.45961
0.17254
i-95
0.25183
0.08092
0.30358
0.08202
0.35609
0.08331
0.40949
0.08482
0.46391
0.08654
2.0
0.25261
0.00
0.30452
0.00
0.35719
0.00
0.41075
0.00
0.46534
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (0.4 + i 0) = 0.41075 + i o.
sinh (0.4 + i 1) = o. + * 1. 08107.
[,43]
Table VII. HYPERBOLIC SINES, sinh (x + iq) - * + if. Continued
x = 0.5
* = -55
a; = 0.6
0.65
x = 0.7
0.52110
0.00
0.57815
0.00
0.63665
0.00
0.69675
0.00
0.75858
0.00
0.05
0.51949
0.08847
0.57637
0.09063
0.63469
0.09301
0.69460
0.09563
0.75625
0.09848
O.I
0.51468
0.17640
0.57103
0.18070
0.62882
0.18545
0.68817
0.19066
0.74925
0.19635
0.15
0.50670
0.26324
0.56218
0.26965
0.61906
0.27674
0.67750
0.28452
0.73763
0.29301
0.2
o.49559
0.34846
0.54986
0.35695
0.60549
0.36633
0.66265
0.37663
0.72146
0.38787
0.25
0.48143
0.43152
0.534H
0.44204
0.58819
0.45366
0.64371
0.46641
0.70084
0.48033
-3
0.46430
o-5"93
0.51514
0.52441
0.56726
0.53819
0.62081
o.55332
0.67590
0.56984
o-3S
0.44431
0.58918
0.49296
0.60354
0.54284
0.61940
0.59408
0.63682
0.64680
0.65582
0.40
0.42158
0.66280
6.46773
0.67895
6.51506
0.69680
0.56368
0.71639
0.61371
0-73777
-45
0.39624
0.73233
0.43963
0.75018
0.48412
0.76990
0.52981
0.79154
0.57683
0.81517
0.5
0.36847
o.79735
0.40882
0.81678
0.45018
0.83825
0.49268
0.86182
0.53640
0.88754
o.55
0.33842
0.85745
o.37548
0.87835
0.41347
0.90144
0.45250
0.92678
0.49266
0.95444
0.6
0.30629
0.91227
0.33983
0.93450
0.37422
0.95906
0.40954
0.98602
0.44589
1 -OI545
0.65
0.27227
0.96146
0.30208
0.98489
0.33265
1.01078
0.36405
1-03919
0.39636
1.07021
0.7
0.23657
1.00472
0.26248
1.02920
0.28904
1.05626
0.31632
1.08595
o.34439
1.11836
o.75
0.19942
1. 04 1 79
0.22125
1.06717
0.24364
1-09523
0.26663
1. 1 2602
0.29030
1. 15962
0.8
0.16103
1.07244
0.17866
1.09857
0.19674
1. 12744
0.21531
1.15912
0.23442
I-I9374
0.85
0.12165
1.09647
0.13497
1.12319
0.14862
1.15271
0.16265
1.18512
0.17709
1.22049
0.9
0.08152
I-H374
0.09044
1. 14088
0.09959
1.1 7087
0.10900
1.20379
0.11867
1.23972
0.9S
0.04088
1.12415
0.04536
i.i5 I 54
0.04995
1.18181
0.05467
1. 21504
0.05952
1. 25130
1.0
0.00
1. 12763
0.00
1.15510
0.00
1. 18547
0.00
1. 21879
0.00
I-255I7
1.05
0.04088
1.12415
0.04536
i-i5i54
0.04995
1.18181
0.05467
1. 21504
0.05952
1. 25130
1.1
0.08152
I-H374
0.09044
1. 1 4088
009959
1. 1 7087
0.10900
1.20379
0.1 1867
1.23972
i-i5
0.12165
1.09647
0.13497
1.12319
0.14862
1.15271
0.16265
1.18512
0.17709
1.22049
1.2
0.16103
1.07244
0.17866
1.09857
0.19674
1. 12744
0.21531
1.15912
0.23442
!-!9374
I.25
0.19942
1. 04 1 79
0.22125
1.06717
0.24364
1-09523
0.26663
1. 12602
0.29030
1. 15962
i-3
0.23657
1.00472
0.26248
1.02920
0.28904
1.05626
0.31632
1.08595
o.34439
1.11836
i-35
0.27227
0.96146
0.30208
0.98489
0.33265
1.01078
0.36405
1-03919
0.39636
1.07021
1.4
0.30629
0.91227
0.33983
o.9345o
0.37422
0.95906
0.40954
0.98602
0.44589
1 -OI545
1 45
0.33842
0.85745
o.37548
0.87835
0.41347
0.90144
0.45250
0.92678
0.49266
0.95444
i-5
0.36847
o.79735
0.40882
0.81678
0.45018
0.83825
0.49268
0.86182
0.53640
0.88754
i-55
0.39624
0.73233
0.43963
0.75018
0.48412
0.76990
0.52981
o.79i54
0.57683
0.81517
1.6
0.42158
0.66280
0.46773
0.67895
0.51506
0.69680
0.56368
0.71639
0.61371
0-73777
1.6s
0.44431
0.58918
0.49296
0.60354
0.54284
0.61940
0.59408
0.63682
0.64680
0.65582
i-7
0.46430
0.5 1 193
0.51514
0.52441
0.56726
0.53819
0.62081
0.55332
0.67590
0.56984
i-75
0.48143
0.43152
o.534i4
0.44204
0.58819
0.45366
0.64371
0.46641
0.70084
0.48033
1.8
0-49559
0.34846
0.54986
0.35695
0.60549
0.36633
0.66265
0.37663
0.72146
0.38787
1.8S
0.50670
0.26324
0.56218
0.26965
0.61906
0.27674
0.67750
0.28452
0.73763
0.29301
1.9
0.51468
0. 1 7640
0.57103
0.18070
0.62882
0.18545
0.68817
0.19066
0.74925
0.19635
i-9S
0.51949
0.08847
0.57637
0.09063
0.63469
0.09301
0.69460
0.09563
0.75625
0.09848
2.0
0.521:0
0.00
0.57815
0.00
0.63665
0.00
0.69675
0.00
0.75858
0.00
Note.
Negative quantities are in heavy type.
Examples, sinh (0.65 + i o.75 ) = 0.26663 + 1. 12602.
sinh (0.55 + i 1.40) = -0.33983 + * 0.93450.
[44]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
x = 0.75
x = 0.8
x = 0.85
* = 0.9
* = 0.95
0.82232
0.00
0.8881 1
0.00
0.95612
0.00
1.02652
0.00
1.09948
0.00
0.0s
0.81978
0.10158
0.88537
0.10493
0.953I7
0.10855
1-02335
0.1 1 244
1.09610
0.11661
O.I
0.81219
0.20253
0.87717
0.20922
0.94435
0.21643
1.01388
0.22418
1.08595
0.23250
0.15
0.79960
0.30224
0.86357
0.31222
0.92970
0.32298
0.99816
0-33455
1. 069 1 1
0.34695
0.2
0.78207
0.40079
0.84464
0.41329
0.90932
0.42753
0.97628
0.44285
1.04567
0.45927
0.25
0.75972
0.4954S
0.82050
0.51182
0.88334
o-52945
0.94838
0.54842
1-01579
0.56875
o-3
0.73269
0.58777
0.79131
0.60718
0.85191
0.62811
0.91463
0.65061
0.97965
0.67473
0-3S
0.701 14
0.67647
o.75724
0.69881
0.81522
0.72289
0.87525
0.74879
0-93747
0.77655
0.4
0.66527
0.76100
0.71849
0.78613
o.7735i
0.81322
0.83047
0.84235
0.88950
0.87358
0-4S
0.62529
0.84083
0.67532
0.86859
0.72704
0.89853
0.78057
0.93071
0.83605
0.96523
0.5
0.58146
0.91548
0.62799
0.94571
0.67608
0.97830
0.72586
I-OI334
o.77745
1.05092
-55
0.53405
0.98449
0.57678
1.01700
0.62095
1.05205
0.66667
1.08973
0.71406
1.13013
0.6
0.48335
1.04742
0.52202
1.08201
0.56199
1-11930
0.60337
I-I5939
0.64621
1.20238
0.65
0.42966
1. 10390
0.46403
1-14035
0.49957
1. 17965
0.53635
1.22191
o.57448
1.26722
0.7
o.37332
I-I5356
0.40319
1.19166
0.43407
1.23274
0.46603
1.27689
0.49916
1-32425
o-75
0.31469
1.19613
0.33986
1-23563
0.36589
1.27822
0.39283
1.32400
0.42076
1.37309
0.8
0.25411
1. 23132
0.27444
1. 27198
0.29546
1.31582
0.31721
1.36294
0.33976
1-41348
0.85
0.19197
1. 25891
0.20732
1.30048
0.22320
1-34530
0.23964
1 -39349
0.25667
1.44516
0.9
0.12864
1.27874
0.13893
1.32097
0.14957
1.36650
0.16058
1. 41 544
0.17200
1.46793
o-95
0.06452
1.29069
0.06968
J-3333 1
0.07502
1.37927
0.08054
1.42867
0.08627
1. 48 1 64
1.0
0.00
1.29468
0.00
1-33743
0.00
I-38353
0.00
I-43309
0.00
1.48623
1.05
0.06452
1.29069
0.06968
I-3333I
0.07502
1.37927
0.08054
1.42867
0.08627
1. 48 1 64
1.1
0.12864
1.27874
0.13893
1.32097
0.14957
1.36650
0.16058
1.41544
0.17200
1.46793
i-i5
0.19197
1. 25891
0.20732
1.30048
0.22320
1-34530
0.23964
1-39349
0.25667
1. 445 16
1.2
0.25411
1. 23132
0.27444
1. 27198
0.29546
1.31582
0.31721
1.36294
0.33976
1. 4 1 348
1-25
0.31469
1.19613
0.33986
1-23563
0.36589
1.27822
0.39283
1.32400
0.42076
1-37309
i-3
0.37332
I-I5356
0.40319
1.19166
0.43407
1.23274
0.46603
1.27689
0.49916
1-32425
i-35
0.42966
1. 10390
0.46403
1-14035
0.49957
1-17965
0.53635
1.22191
0.57448
1.26722
1.4
0.48335
1.04742
0.52202
1. 08 20 1
0.56199
1-11930
0.60337
I-I5939
0.64621
1.20238
i-4S
0.53405
0.98449
0.57678
1.01700
0.62095
1.05205
0.66667
1.08973
0.71406
1.13013
i-5
0.58146
0.91548
0.62799
0.94571
0.67608
0.97830
0.72586
i-oi334
o.77745
1.05092
i-55
0.62529
0.84083
0.67532
0.86859
0.72704
0.89853
0.78057
0.93071
0.83605
0.96523
1.6
0.66527
0.76100
0.71849
0.78613
0.77351
0.81322
0.83047
0.84235
0.88950
0.87358
1.65
0.70114
0.67647
0.75724
0.69881
0.81522
0.72289
0.87525
0.74879
0.93747
0.77655
i-7
0.73269
0.58777
0.79131
0.60718
0.85191
0.62811
0.91463
0.65061
0.97965
0.67473
i-75
0.75972
o.49545
0.82050
0.51182
0.88334
0.52945
0.94838
0.54842
1.01579
0.56875
1.8
0.78207
0.40079
0.84464
0.41329
0.90932
0.42753
0.97628
0.44285
1.04567
0.45927
1.8s
0.79960
0.30224
0.86357
0.31222
0.92970
0.32298
0.99816
o.33455
1. 069 1 1
0.34695
1.9
0.81219
0.20253
0.87717
0.20922
0.94435
0.21643
1. 01388
0.22418
1.08595
0.23250
i-95
0.81978
0.10158
0.88537
0.10493
o.953i7
0.10855
1.02335
0.1 1 244
1. 09610
0.11661
2.0
0.82232
0.00
0.8881 1
0.00
0.95612
0.00
1.02652
0.00
1.09948
0.00
Note.
Negative quantities are in heavy type.
Examples, sinh (0.8 + ?'o.7) = 0.40319 + i 1.19166.
sinh (0.8 + i 1.7) = 0.79131 + io.6o7i{
[45]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
x = 1.05
x = 1. 15
1.17520
0.00
1.25386
0.00
I-33565
0.00
1.42078
0.00
1.50946
0.00
0.05
1.17158
0.12107
1.24999
0.12583
I-33I53
0.13091
1. 4 1 640
0.13632
1.50481
0.14206
O.I
1. 16073
0.24139
1.23842
0.25089
1.31920
0.26101
1.40329
0.27179
1.49088
0.28325
0.15
1. 14273
0.36023
1.21921
0.37440
1.29875
0.38951
1-38152
0.40559
1.46776
0.42269
0.2
1.11768
0.47684
1. 19249
0.49560
1.27028
0.51560
I-35I24
0.53689
1-43558
0-55952
0.25
1.08574
0.59051
1-15841
0.61375
1.23398
0.63852
1. 3 1 263
0.66488
L39456
0.69291
o-3
1.047 1 1
0.70055
1.11719
0.72811
1. 19007
0-75749
1.26592
0.78877
1-34494
0.82202
o-3S
1.00202
0.80626
1.06909
0.83798
1.13883
0.87180
1.21141
0.90780
1.28703
0.94607
0.4
0.95076
0.90700
1.01439
0.94269
1.08056
0.98073
1. 14943
1.02123
1.22118
1.06428
0-4S
0.89363
1.00215
o.95344
1. 04 1 58
1.01564
1.08362
1.08037
1. 12836
1.14781
I-7I593
-5
0.83099
1.09112
0.88661
1-13405
0-94445
1. 17982
1 .00464
1.22854
1.06735
1.28033
o.55
0.76323
I-I7337
0.81432
I-2I953
0.86743
1.26875
0.92272
1.32114
0.98032
1.37684
0.6
0.69077
1.24838
0.73700
1.29750
0.78508
1.34986
0.83511
1.40560
0.88724
1.46485
0.65
0.61404
1-31569
0.65514
1.36746
0.69787
1.42265
o.74235
1-48139
0.78869
1.54384
0.7
o-533S3
1.37490
0.56924
1.42899
0.60637
1.48666
0.64502
1.54805
0.68528
1.61331
0-7S
o-44973
1.42562
0.47983
1.48171
0.51113
I-54I5I
o.5437i
1-60517
o.57765
1.67283
0.8
0.36316
1.46756
0.38746
1-52530
0.41274
1.58685
0.43904
1.65238
0.46645
1.72204
0.85
0.2743S
1.50045
0.29271
1-55948
0.31 180
1.62242
0.33167
1. 68941
0.35238
1.76063
0.9
0.18384
1.52408
0.19615
1.58405
0.20894
1.64798
0.22226
1. 71602
0.23613
1.78836
o-95
0.09221
1-53832
0.09838
1.59885
0.10479
1.66337
0.11147
1.73206
0.1 1843
1.80507
1.0
0.00
1.54308
0.00
1.60379
0.00
1.66852
0.00
I-7374I
0.00
1.81066
1. 05
0.09221
1-53832
0.09838
1.59885
0.10479
1.66337
0.11147
1.73206
0.11843
1.80507
1.1
0.18384
1.52408
0.19615
1.58405
0.20894
1.64798
0.22226
1. 71602
0.23613
1.78836
i-i5
0.27435
1.50045
0.29271
I.55948
0.31180
1.62242
0.33167
1. 6894 1
0.35238
1.76063
1.2
0.36316
1.46756
0.38746
!-52530
0.41274
1.58685
0.43904
1.65238
0.46645
1.72204
1. 25
0-44973
1.42562
0.47983
1.48171
0.51113
I.54I5I
0.54371
1.605 1 7
0.57765
1.67283
i-3
0-53353
1.37490
0.56924
1.42899
0.60637
1.48666
0.64502
1.54805
0.68528
1-61331
i-3S
0.61404
i-3!569
0.65514
1.36746
0.69787
1.42265
0.74235
1.48139
0.78869
I.54384
1.4
0.69077
1.24838
0.73700
1.29750
0.78508
1.34986
0.8351 1
1.40560
0.88724
1.46485
i-45
0.76323
I-I7337
0.81432
I-2I953
0.86743
1.26875
0.92272
1.32114
0.98032
1.37684
i-5
0.83099
1.09112
0.88661
1-13405
0.94445
1. 17982
1.00464
1.22854
1-06735
1.28033
i-55
0.89363
1.00215
0.95344
1. 041 58
1. 01564
1.08362
1.08037
1. 12836
1.14781
I-I7593
1.6
0.95076
0.90700
1. 01 439
0.94269
1.08056
0.98073
1. 14943
1.02123
1.22118
1.06428
1.6S
1.00202
0.80626
1.06909
0.83798
1. 13883
0.87180
1.21141
0.90780
1.28703
0.94607
i-7
1.04711
0.70055
1.11719
0.72811
1. 19007
o.75749
1.26592
0.78877
1-34494
0.82202
i-7S
1.08574
0.59051
1.15841
0.61375
1.23398
0.63852
1.31263
0.66488
1-39456
0.69291
1.8
1.11768
0.47684
1. 19249
0.49560
1.27028
0.51560
1-35124
0.53689
1-43558
o.55952
1.8S
1. 14273
0.36023
1.21921
0.37440
1.29875
0.38951
1.38152
0.40559
1.46776
0.42269
1.9
1. 16073
0.24139
1.23842
0.25089
1. 31920
0.26101
1.40329
0.27179
1.49088
0.28325
i-95
1.17158
0.12107
1.24999
0.12583
1-33 1 53
0.1 309 1
1 .41640
0.13632
1. 50481
0.14206
2.0
1. 17520
0.00
1.25386
0.00
133565
0.00
1.42078
0.00
1.50946
0.00
Note.
Negative quantities are in heavy type.
Examples, sinh (1.0 + i i.o) = o 4- i 1.54308.
sinh (1.0 + i 1.5) = 0.83099 + * 1.09112.
[46]
Table -VII. HYPERBOLIC SINES, sinh (* + iq) = u + iv. Continued
0.05
O.I
0.15
0.2
0.25
-3
o-35
0.4
o.45
o-5
o-55
0.6
0.65
0.7
o.75
0.8
0.85
0.9
o-95
1.0
1.05
1.1
1.2
1-25
i-3
i-35
1.4
i-45
i-5
i-S5
1.6
1.65
i-7
i-7S
1.8
1.8s
1.9
1 -95
1. 60192
1.59698
1.58220
1-55766
I-52352
1-25
0.00
0.14816
0.29541
0.44084
o-58355
* = 1.3
1.47998 0.72267
1.42732 0.85733
1.36586 0.98670
1.29598 1. 10999
1.21811 1.22643
1. 13273
1.04036
0.94158
0.83700
0.72726
0.61303
0.49502
0.37396
0.25060
0.12569
0.00
0.12569
0.25060
0.37396
0.49502
0.61303
0.72726
0.83700
0.94158
1.04036
1-13273
1.21811
1.29598
1.36586
1.42732
1.47998
1-52352
1-55766
1.58220
1.59698
33532
43597
52777
.61014
.68260
.74467
.79600
.83624
.86517
.88260
,88260
86517
,83624
,79600
,74467
.68260
,61014
52777
43597
33532
.22643
.10999
0.98670
0.85733
0.72267
o-58355
0.44084
0.29541
0.14816
1.69838
1-69315
1.67747
1. 65 146
1.61526
0.00
0.15464
0.30832
0.46010
0.60905
1.56910 0.75424
1.51327 0.89478
1. 448 1 1
1.37402
1. 29146
1.20094
1.10301
0.99829
0.88740
0.77105
0.64994
0.52483
0.39648
0.26569
0.13325
0.00
0.13325
0.26569
0.39648
0.52483
0.64994
0.77105
0.88740
0.99829
1.10301
1.20094
1. 29146
1.37402
1. 4481 1
.02980
.15848
.28001
39365
.49870
59451
.75610
.82089
87445
.91646
94665
.96484
.97091
.96484
94665
.91646
87445
.82089
.75610
59451
.49870
3936S
.28001
.15848
.02980
1. 51327 0.89478
1. 56910
1. 61526
1.65146
1.67747
1-69315
0.75424
0.60905
0.46010
0.30832
0.15464
* = i-35
1.79909 0.00
1.79354 0.16150
1.77694 0.32199
1.74938 0.48051
1. 71 104 0.63606
1.66215
1.60300
I-53398
i-4555o
1.36804
1. 27215
1. 16842
1.05748
0.94002
0.81677
0.78769
0.93446
1.07548
1.20986
1-33678
1.45546
1-56517
1.66523
I-75502
I-83399
0.68848 1. 90165
o-55595 1-95759
0.41999 2.00146
0.28144 2.03299
0.14116 2.05199
0.00 2.05833
0.14116 2.05199
0.28144 2.03299
0.41999 2.00146
0-55595 1-95759
0.68848 1. 90165
0.81677 1-83399
0.94002 1.75502
1.05748 1.66523
1. 16842 1.56517
1. 27215
1.36804
1-45550
1.53398
1.60300
1.66215
1.71104
1.74938
1.77694
1-79354
1-45546
1.33678
1.20986
1.07548
0.93446
0.78769
0.63606
0.48051
0.32199
0.16150
1.90430
1.89843
1.88086
1.85169
1.81110
1-75934
1.69675
1.62369
1. 5406 1
1.44804
I-34655
1.23674
1-11932
0.99500
0.86454
0.72875
0.58846
0.44455
0.29790
0.14427
0.00
0.14427
0.29790
o.44455
0.58846
0.72875
0.86454
0.99500
1.11932
1.23674
I.34655
1.44804
1. 54061
1.62369
1.69675
1-75934
1 .81110
1.85169
1.88086
1.89843
1.4
O.00
0.16876
0.33647
0.50212
0.66466
0.82311
0.97649
1. 1 2384
1.26427
I.39690
1.52092
I-63556
1. 7401 2
1-83394
1. 9 1 646
1-98717
2.04562
2.09147
2.12442
2.14427
2.15090
2.14427
2.12442
2.09147
2.04562
I.987I7
1. 9 1 646
1.83394
1. 7401 2
I-63556
1.52092
1.39690
1.26427
1-12384
0.97649
0.82311
0.66466
0.50212
0.33647
0.16876
x - 1.45
2.01427
2.00806
I.98947
I.95862
I.91569
I.86094
1-79473
I-7I745
1.62958
1. 53 166
1.4243 1
1.30817
1. 18396
1.05245
0.91446
0.77083
0.62244
0.47022
0.31510
0.15804
0.00
0.15804
0.31510
0.47022
0.62244
0.77083
0.91446
1.05245
1. 18396
1.30817
1.42431
1. 53 1 66
1.62958
I-7I745
1-79473
1.86094
1. 9 1 569
1.95862
1.98947
2.00806
0.00
0.17644
0.35180
0.52498
0.69493
0.86060
1.02095
1. 17502
1.32184
1. 4605 1
1. 5901 7
1. 7 1007
I-8I935
I-9I745
2.00373
2.07766
2.13878
2.18671
2.22115
2.24191
2.24884
2.24191
2.22115
2.18671
2.13878
2.07766
2.00373
I-9I745
I-8I935
1. 71007
I-590I7
1. 4605 1
1.32184
1. 17502
1.02095
0.86060
0.69493
0.52498
0.35180
0.17644
2.0 1. 60192 0.00
1.69838 0.00
1.79909 0.00
1.90430 0.00
2.01427 0.00
Note. Negative quantities are in heavy type.
Examples, sinh (1.35 + io) = 1.70909 -f- io.
sinh (1.4 + i 1. 15) = 0.44455 + i 2.09147.
[47]
Table VII. HYPERBOLIC SINES, sinh (x + iq) m u + iv. Continued
*= i.S
i-5S
* = 1.6
x = 1.65
x = 1.7
2.12928
0.00
2.24961
0.00
2-37557
0.00
2.50746
0.00
2.64563
0.00
0.0s
2.12272
0.18457
2.24268
0.19316
2.36824
0.20223
2-49973
0.21180
2.63747
0.22191
O.I
2.10307
0.36800
2.22191
0.38512
2.34632
0.403 20
2.47659
0.42230
2.61306
0.44245
0.15
2.07045
0.54916
2.18745
o.5747i
2.30993
0.60170
2.43818
0.63019
2-57253
0.66026
0.2
2.02507
0.72693
2.I395I
0.76076
2.25930
0.79648
2.38474
0.83420
2.51614
0.87400
0.25
1.96720
0.90023
2.07837
0.942 1 1
2.19473
0.98636
2.31660
1.03306
2.44424
1.08235
o-3
1.89720
1*06797
2.00442
1. 1 1 766
2.11664
1.17015
2.23417
1.22556
2.35727
1.28403
o-3S
1-81551
1. 22913
1.91811
1.28632
2.02550
1.34672
2.13797
1.41050
2.25577
1-47779
0.4
1.72263
1.38271
1.81997
1.44704
1.92187
1-51500
2.02858
1.58674
2.14036
1.66244
0-4S
1.61912
1.52777
1. 71062
1.59885
1.80640
1.67393
1.90669
1.75320
2.01175
1.83684
-5
1-50563
1.66341
1-59071
1.74080
1.67978
1.82254
I.77305
1.90885
1.87074
1.99992
-55
1.38286
1.78879
1.46101
1.87201
1. 54281
1.95992
1.62847
2.05274
1. 71820
2.15067
0.6
1. 25156
1-90314
1.32229
1. 99169
1.39632
2.08522
1-47385
2.18396
i-555o6
2.28816
0.65
1-11255
2.00576
I-I7542
2.09908
1. 24123
2.19765
1-31015
2.30173
1.38234
2.41154
0.7
0.96667
2.09601
1.02130
2-19353
1.07848
2.29654
1-13837
2.40529
1. 20109
2.52005
-75
0.81484
2.17334
0.86089
2.27446
0.90909
2.38127
0-95957
2.49404
1. 01 244
2.61302
0.8
0.65798
2.23727
0.69517
2.34137
o.734C9
2.45131
0.77485
2.56740
0.81754
2.68989
0.85
0.49707
2.28742
0.52516
2.39384
o.55456
2.50625
0.58536
2.62494
0.61761
2.75017
0.9
0-33309
2.32345
0.35192
2.43I55
0.37163
2-54573
0.39225
2.66629
0.41387
2.79350
o-95
0.16706
2.345 J 6
0.17650
2.45427
0.18639
2.56952
0.19673
2.69121
0.20757
2.81960
1.0
0.00
2-35241
0.00
2.46186
0.00
2.57746
0.00
2.69951
0.00
2.82832
1.05
0.16706
2.34516
0.17650
2.45427
0.18639
2.56952
0.19673
2.69121
0.20757
2.81960
1.1
0.33309
2.32345
0.35192
2.43I55
0.37163
2-54573
0.39225
2.66629
0.41387
2-79350
i-i5
0.49707
2.28742
0.52516
2.39384
0.55456
2.50625
0.58536
2.62494
0.61761
2.75017
1.2
0.65798
2.23727
0.69517
2 .34i37
0.73409
245131
0.77485
2.56740
0.81754
2.68989
1.25
0.81484
2-17334
0.86089
2.27446
0.90909
2.38127
0.95957
2.49404
1. 01244
2.61302
!-3
0.96667
2.09601
1. 02130
2-19353
1.07848
2.29654
1-13837
2.40529
1. 20109
2.52005
i-3S
1.11255
2.00576
1. 17542
2.09908
1. 24123
2.19765
1.31015
2.30173
1.38234
2.4II54
1.4
1.25156
1.903 14
1.32229
1. 99 1 69
1.39632
2.08522
I.47385
2.18396
1-55506
2.28816
1 -45
1.38286
1.78879
1.46101
1. 87201
1. 54281
1.95992
1.62847
2.05274
1. 71820
2.15067
i-5
150563
1.66341
1-59071
1.74080
1.67978
1.82254
I-77305
1.90885
1.87074
1.99992
i-5S
1.61912
1.52777
1. 71062
1.59885
1.80640
1-67393
1.90669
1.75320
2.01 175
1.83684
1.6
1.72263
1-38271
1.81997
1.44704
1.92187
1. 51500
2.02858
1.58674
2.14036
1.66244
1.6s
1.81551
1. 22913
1.91811
1.28632
2.02550
1.34672
2.13797
1.41050
2.25577
1.47779
i-7
1.89720
1.06797
2.00442
1.11766
2.1 1664
1.17015
2.23417
1.22556
2.35727
1.28403
i-7S
1.96720
0.90023
2.07837
0.9421 1
2.19473
0.98636
2.31660
1.03306
2.44424
1.08235
1.8
2.02507
0.72693
2.13951
0.76076
2.25930
0.79648
2.38474
0.83420
2.51614
0.87400
1.8s
2.07045
0.54916
2.18745
o.5747i
2.30993
0.60170
2.43818
0.63019
2.57253
0.66026
1.9
2.10307
0.36800
2.22191
0.38512
2.34632
0.40320
2.47659
0.42230
2.61306
0.44245
i-9S
2.12272
0.18457
2.24268
0.19316
2.36824
0.20223
2.49973
0.21180
2.63747
0.22191
2.0
2.12928
0.00
2.24961
0.00
2-37557
0.00
2.50746
0.00
2.64563
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (1.7 + i 0.7) = 1. 20109 + i 2.52005.
sinh (1.7 + i 1^2) = -2.35727 + i 1.28403.
[48]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
x = i. 75
x = 1.85
* = 1.9
x = 1.95
2.79041
0.00
2.94217
0.00
3.10129
0.00
3.26816
0.00
3-44321
O.00
0.05
2.78181
0.23257
2.93310
0.24381
3-09I73
0.25566
3.25809
0.26815
343259
0.28131
O.I
2.75606
0.46370
2.90595
0.48612
3.063 1 1
0.50975
3-22793
0-53465
3.40081
0.56089
0.15
2.71331
0.69198
2.86088
0.72542
3.01560
0.76069
3.17787
0.79785
3-34807
0.83701
0.2
2.65384
0.91599
2.79817
0.96026
2.94950
1.00694
3.10821
1.05614
3.27468
1. 10797
0.25
2.57800
I-I3435
2.71821
1.18918
2.86522
1.24698
3-OI939
1.30791
3.18111
1.37210
0.3
2.48627
I-3457I
2.62149
1.41076
2.76327
1-47934
2.91196
1.55162
3.06792
1.62777
o-3S
2.37922
1.54878
2.50862
1.62365
2.64429
1.70258
2.78657
1.78576
2.93582
I.8734I
0.4
2.25749
1. 74231
2.38027
1.82653
2.50900
I-9I53I
2.64400
2.00889
2.78561
2.10749
o.45
2.12185
1.92509
2.23725
2.01814
2.35824
2.11624
248513
2.21964
2.61823
2.32858
0.5
1.97312
2.09600
2.08043
2.19731
2.19294
2.30413
2.31094
2.41670
2.43471
2-53532
o-55
1.81223
2-25399
1.91079
2.36294
2.01413
2.47780
2.12250
2.59887
2.23618
2.72642
0.6
1. 640 1 6
2.39808
1.72937
2.51400
1.82289
2.63620
1.92098
2.76501
2.02387
2.90071
0.65
1-45799
2-52739
I-53728
2.64956
1.62042
2-77835
1. 70761
2.91409
1.79907
3.057I3
0.7
1.26682
2.64111
1-33572
2.76878
1.40796
2.90337
1.48372
3.04522
1.56318
3.19469
0-7S
1.06784
2.73855
1. 12592
2.87093
1.18681
3.01049
1.25067
3-15757
1.31766
3-31255
0.8
0.86229
2.81911
0.90918
2-95538
0.95835
3.09904
1.00992
3-25045
1. 0640 1
3.41000
0.85
0.65141
2.88229
0.68684
3.02161
0.72398
3.16850
0.76294
3-32330
0.80380
3.48641
0.9
0.43652
2.92769
0.46026
3.06921
0.48627
3-21841
0.51125
3-37565
0.53864
3.54I34
o.95
0.21893
2.95505
0.23084
3.09789
0.24332
3.24848
0.25642
3.40719
0.27015
3-57443
1.0
0.00
2.96419
0.00
3.10747
0.00
3-25853
0.00
341773
0.00
3.58548
1. 05
0.21893
2-95505
0.23084
3.09789
0.24332
3.24848
0.25642
3.40719
0.27015
3-57443
1.1
0.43652
2.92769
0.46026
3.06921
0.48627
3-21841
0.51125
3.37565
0.53864
3-54134
i-i5
0.65141
2.88229
0.68684
3.02161
0.72398
3.16850
0.76294
3-32330
0.80380
3.48641
1.2
0.86229
2.81911
0.90918
2-95538
0.95835
3.09904
1.00992
3-25045
1. 0640 1
3.41000
1.25
1.06784
2.73855
1. 12592
2.87093
1.18681
3.01049
1.25067
3-15757
1. 3 1 766
3-31255
i-3
1.26682
2.64111
1-33572
2.76878
1.40796
2.90337
1.48372
3.04522
1.56318
3.19469
i-35
1-45799
2.52739
1.53728
2.64956
1.62042
2.77835
1. 70761
2.91409
1.79907
3.o57i3
1.4
1. 64016
2.39808
I.72937
2.51400
1.82289
2.63620
1.92098
2.76501
2.02387
2.90071
i-4S
1. 81223
2-25399
1. 9 1 079
2.36294
2.01413
2.47780
2.12250
2.59887
2.23618
2.72642
i-5
1.97312
2.09600
2.08043
2.19731
2.19294
2.30413
2.31094
2.41670
2.43471
2.53532
i-55
2.12185
1.92509
2.23725
2.01814
2.35824
2.11624
2.48513
^2.21964
2.61823
2.32858
1.6
2.25749
1. 74231
2.38027
1.82653
2.50900
I-9I53I
2.64400
2.00889
2.78561
2.10749
1.65
2.37922
1.54878
2.50862
1.62365
2.64429
1.70258
2.78657
1.78576
2.93582
i.8734i
i-7
2.48627
1 -345 7 1
2.62149
1.41076
2.76327
1-47934
2.91196
1.55162
3.06792
1.62777
i-75
2.57800
I-I3435
2.71821
1,18918
2.86522
1.24698
301939
1. 30791
3.18111
1.37210
1.8
2.65384
0.91599
2.79817
0.96026
2.94950
1.00694
3.10821
1.05614
3-27468
1. 10797
1.85
2.71331
0.69198
2.86088
0.72542
3.01560
0.76069
3.17787
0.79785
3-34807
0.83701
1.9
2.75606
0.46370
2.9059S
0.48612
3.0631 1
0.50975
322793
0.53465
3.40081
0.56089
i-95
2.78181
0.23257
2.93310
0.24381
309173
0.25566
3.25809
0.26815
343259
0.28131
2.0
2.79041
0.00
2.94217
0.00
3.10129
0.00
3.26816
0.00
3-44321
0.00
Note.
Negative quantities are in heavy type.
Examples, sinh (1.85 + ^ 0.75) = 1.18681 + i 3-01049.
sinh (1.85 + i i-35) = -1.62042 + i 2.77835.
[49]
Table VII. HYPERBOLIC SINES, sinh (* 4- iq) = it + iv. Continued
x = 2.05
* = 2.15
3.62686
0.00
3-8I958
0.00
4.02186
0.00
4.23419
0.00
4-457"
O.00
0.05
3-61568
0.29518
3.80781
0.30978
4.00946
0.32516
4-22113
o.34i35
4-44337
0.35839
O.I
3.58221
0.58854
3.77256
0.61765
3-97235
0.64831
4.18206
0.68060
4.40223
0.71458
0.15
3.52666
0.87827
3.71404
0.92172
3.91074
0.96747
4-11720
1.01564
4-33396
1.06636
0.2
3-44935
1. 16258
3.63264
I. 22010
3.82501
1.28066
4.02695
1-34443
4.23896
1.41156
0.25
3-35078
1-43973
3-52883
1.51096
3-7I57I
1.58596
3.91188
1.66493
4.1 1783
1.74806
-3
3- 2 3 I 5 6
I.70800
3-40327
I.79250
3-5835I
1.88148
3.77269
1.97516
3.97I3I
2.07379
o.35
3.09241
I.96574
3-23673
2.06299
3.42920
2.16540
3.61024
2.27322
3.80031
2.38672
0.4
2.93420
2.21136
3.0901 1
2.32076
3-25376
2-43597
342553
2.55726
3.60588
2.68495
o.4S
2.75789
2-44335
2.90443
2.56423
3-05825
2.69152
3.21970
2.82553
3.38921
2.96661
-5
2.56458
2.66027
2.70085
2.79188
2.84389
2.93048
2.99402
3.07639
3-i5i65
3.23000
o-S5
2.35546
2.86080
2.48062
3.00232
2.61199
3-I5I37
2.74988
3.30828
2.89466
3-47347
0.6
2.13182
3.04368
2.24509
3.19426
2.36399
3-35283
2.48879
3.5I977
2.61982
3-69552
0.65
1.89503
3.20780
1-99573
3-36649
2.10142
3-5336i
2.21236
3-70956
2.32883
3.89478
0.7
1.64656
3-35214
I.73405
3.5I798
I.82589
3.69261
1.92228
3.87647
2.02349
4.07003
o-75
1.38794
347581
1. 46 1 69
3-64777
I-539IO
3.82885
1.62035
4.01950
1.70566
4.22019
0.8
1. 12076
3.57806
1. 18032
3.75507
1.24282
3.94148
1.30844
4-13773
1-37732
4-34433
0.85
0.84667
3-65825
0.89166
3.83923
0.93888
4.02981
0.98845
4.23046
1 .04049
4.44170
0.9
0.56737
3-7I587
o.5975i
3.89971
0.62916
4.09329
0.66237
4-29711
0.69724
4.51167
o-9S
0.28456
3-75059
0.29968
3.936I5
0.31555
4-I3I54
0.33221
4.33726
o.3497o
4-55382
1.0
0.00
3.76220
0.00
3.94832
0.00
4-I443I
0.00
4-35067
0.00
4.56791
1. 05
0.28456
3.75059
0.29968
3.936I5
0.3I555
4-I3I54
0.33221
4.33726
0.34970
4-55382
1.1
0.56737
3-71587
o.5975i
3.89971
0.62916
4.09329
0.66237
4-29711
0.69724
4.51167
"5
0.84667
3-65825
0.89166
3-839 2 3
0.93888
4.02981
0.98845
4.23046
1.04049
4.44170
1.2
1. 12076
3.57806
1. 18032
3-75507
I.24282
3.94148
1.30844
4-13773
1-37732
4-34433
1.25
1.38794
3.4758i
1. 46 1 69
3-64777
I-539IO
3-82885
1.62035
4.01950
1.70566
4.22019
1-3
1.64656
3-35214
1-73405
3-5I798
1.82589
3.69261
1.92228
3.87647
2.02349
4.07003
i-3S
1.89503
3.20780
1-99573
3-36649
2.10142
3-5336i
2.21236
3-70956
2.32883
3.89478
1.4
2.13182
3.04368
2.24509
3.19426
236399
3-35283
2.48879
3-51977
2.61982
3-69552
i-45
2.35546
2.86080
2.48062
3.00232
2.61199
3-I5I37
2.74988
3.30828
2.89466
3-47347
1-5
2.56458
2.66027
2.70085
2.79188
2.84389
2.93048
2.99402
3.07639
3-15165
3.23000
i-55
2.75789
2-44335
2.90443
2.56423
3.05825
2.69152
321970
2.82553
338921
2.96661
1.6
2.93420
2.21136
3.0901 1
2.32076
325376
2-43597
3.42553
2.55726
3.60588
2.68495
1.6S
3.09241
1.96574
3-23673
2.06299
3.42920
2.16540
3.61024
2.27322
3-80031
2.38672
i-7
3-23156
1.70800
3.40327
1.79250
3-5835I
1. 88148
3.77269
1.97516
3.97I3I
2.07379
i-75
3-35078
1-43973
3-52883
1.51096
3-7I57I
1.58596
3.91188
1.66493
4-11783
1.74806
1.8
3-44935
1. 16258
3.63264
1. 22010
3.82501
1.28066
4.02695
1-34443
4.23896
1.41156
1.85
3.52666
0.87827
3.71404
0.92172
3.91074
0.96747
4.11720
1.01564
433396
1.06636
1.9
3.58221
0.58854
3-77256
0.61765
3-97235
0.64831
4.18206
0.68060
4.40223
0.71458
i-9S
3.61568
0.29518
3.80781
0.30978
4.00946
0.32516
4.22113
o-34i35
4-44337
0.35839
2.0
3.62686
0.00
3.81958
0.00
4.02186
0.00
4.23419
0.00
4-4571 1
0.00
Note.
Negative quantities are in heavy type.
Examples, sinh (2.2 + i 1.0) = o + * 4.56791.
sinh (2.2 + * i) = 3.15165 + i 3.23000.
[50]
Table VII. HYPERBOLIC SINES, sinh (x + iq) =u+ iv. Continued
x = 2.25
x = 2.3
x = 2.35
x = 2.4
x = 2.45
4.69117
0.00
4.93696
0.00
5-i95io
0.00
5.46623
0.00
5-75I03
0.00
6.0s
4.67671
o-37633
4.92174
0.39522
5.17909
0.41509
5-44938
0-43599
5-73330
045799
O.I
4-6334I
0.75035
4.87618
0.78799
5-i3ii4
0.82761
5-39893
0.86930
5.68022
0.91316
0.15
4-56i55
1.11974
4.80056
1. 17592
5-05156
1-23504
5-3i52i
1.29724
5-592I3
1.36269
0.2
4.46157
1.48222
4.69533
I-55659
4.94083
1.63485
5.19869
1.71719
546955
1.80383
0.25
4-33407
I-83557
4.56116
1.92766
4-79965
2.02457
5.05014
2.12655
5-3 I 325
2-23385
0.03
4.17986
2.17760
4.39887
2.28685
4.62887
2.40182
4.87045
2.52280
5.12420
2.65009
o-3S
3-99987
2.50620
4.20946
2.63194
4-42955
2.76426
4.66073
2.90349
4-90356
3.04999
0.4
3-79523
2-8i935
3.99409
2.96081
4.20292
3.10966
4.42228
3.26629
4.65268
343109
o.45
3-56719
3.11512
3-754io
3.27141
3-95038
3-43588
4.15656
3.60894
4-373"
3.79104
-5
3.31716
3.39168
3.49096
3-56185
3-6735I
3-74093
3-86521
3-92935
4.06659
4.12761
o-55
3.04677
3.64734
3.20630
3-83034
3-37395
4.02290
3-55003
4-22554
3-73499
4-43873
0.6
2.75740
3.88050
2.90188
4.07520
3-05360
4.28008
3.21297
449567
3-38036
4.72249
0.65
2-45"3
4.08975
2-57956
4.29494
2-71443
4.51087
2.85610
4.73808
3.00490
4-977I3
0.7
2.12975
4-27377
2.24134
4.48820
2-35853
4.71384
2.48162
4-95127
2.61091
5.20109
o.75
I-79523
4-43145
1.88930
4-65378
1.98808
4.88776
2.09184
5-13394
2.20082
5-39298
0.8
1.44965
4.56181
1.52560
4.79058
1-60537
5-03I53
1. 689 1 6
5.28496
1.77716
5-55I62
0.85
1 -95 1 3
4.66404
1-15251
4.89805
1. 21277
5.14429
1.27607
5-4034I
1-34255
5.67603
0.9
0.73386
4-73751
0.77231
4-97521
0.81269
5-22533
0.85511
548853
0.89966
5-76545
o-95
0.36807
4.78178
0.38735
5.02169
0.40760
5.27416
0.42888
5-5398i
0.45122
5-81933
1.0
0.00
4-79657
0.00
5.03722
0.00
5.29047
0.00
5-55695
0.00
5-83732
1.05
0.36807
4.78178
0.38735
5.02169
0.40760
5.27416
0.42888
5-5398i
0.45122
5-8i933
1.1
0.73386
4-73751
0.77231
4-97521
0.81269
5-22533
0.8551 1
548853
0.89966
5-76545
i-i5
1-09513
4.66404
1.15251
4.89805
1. 21277
5.14429
1.27607
540341
1-34255
5.67603
1.2
1.44965
4.56181
1.52560
4.79058
1-60537
5-03I53
1.68916
5.28496
1. 77716
5-55I62
1.25
1-79523
4-43I45
1.88930
4-65378
1.98808
4.88776
2.09184
5-13394
2.20082
5-39298
i-3 '
2.12975
4-27377
2.24134
4.48820
2.35853
4.71384
2.48162
4-95*27
2.61091
5.20109
1-35
2.45113
4.08975
2.57956
4.29494
2.71443
4.51087
2.85610
4.73808
3.00490
4-97713
1.4
2.75740
3-88050
2.90188
4.07520
3.05360
4.28008
321297
449567
338036
4.72249
i-4S
3.04677
3-64734
3.20630
3-83034
3.37395
4.02290
3-55003
4-22554
3-73499
443873
i-5
3-3i7i6
3.39168
3.49096
3.56185
3-67351
3-74093
386521
3-92935
4.06659
4.12761
i-55
3-567I9
3-11512
3-75410
3-27141
395038
3-43588
415656
3.60894
4-373H
3.79104
1.6
3-79523
2-81935
3.99409
2.96081
4.20292
3.10966
4.42228
3.26629
4.65268
343 J 09
1.65
3 99987
2.50620
4.20946
2.63194
442955
2.76426
4.66073
2.90349
490356
3.04999
i-7
4.17986
2.17760
4.39887
2.28685
4.62887
2.40182
4.87045
2.52280
5.12420
2.65009
i-75
4-33407
1-83557
4.56116
1.92766
479965
2.02457
505014
2.12655
5-3I325
2-23385
1.8
4.46157
1.48222
4.69533
I-55659
4.94083
1.63485
519869
1.71719
546955
1.80383
1.85
4-56I55
1.11974
4.80056
1. 17592
5-05156
1-23504
5-31521
1.29724
5-59213
1.36269
1.9
4-6334I
0.75035
4.87618
0.78799
5.i3ii4
0.82761
539893
0.86930
5.68022
0.91316
i-95
4.67671
0.37633
4.92174
0.39522
5.17909
0.41509
5-44938
o-43599
5-7333Q
045799
2.0
4.691 1 7
0.00
4.93696
0.00
5-I95IO
0.00
5.46623
0.00
5.75103
0.00
Note.
Negative quantities are in heavy type.
Examples, sinh (2.4 + i 0.05) = 5.44938 + i 0.43599.
sinh (2.4 + j 1.95) = -5.44938 4- 7*0.43599.
[5i]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
x = 2.5
2-55
X = 2.6
x = 2.65
x = 2.7
6.05020
0.00
6.36451
0.00
6.69473
O.00
7.04169
O.00
7.40626
0.00
0.05
6.03155
0.481 13
6.34489
0.50548
6.67409
0.53109
7.01998
0.55803
7-38343
0.58636
O.I
5-97572
0.95930
6.28615
1.00784
6.61231
1. 0589 1
6.95500
1.11262
7-3i5o8
1.16911
0.15
5.88304
143155
6.18866
I-50399
6.50976
1.58019
6.84713
1.66034
7.20163
1.74465
0.2
5-754o8
1.89498
6.05301
1.99087
6.36706
2.09174
6.69705
2.19784
7-04377
2.30943
0.25
5.58966
2.34673
5.88004
2.46547
6.18512
2-59039
6.50567
2.72178
6.84249
2.85997
o-3
5-39077
2.78401
5.67082
2.92488
5-96505
3.07306
6.27419
3.22894
6-59903
3.39288
0-3S
5-15865
3-20411
5.42664
3.36624
5.70819
3-5368o
6.00403
3.71619
6.31488
3.90488
0.4
4.89472
3.60448
5.14900
3.78686
5-4i6i5
3.97872
5.69685
4-18053
5-99*79
4-39279
-45
4.60062
3.98260
4.83961
4-18413
5.09071
4.39612
5-35454
4.61910
5-63I77
4-85363
-5
4.27814
4-336i9
4-50039
4-5556o
4-73389
4.78641
4-97923
5.02919
5.23702
5-28454
-55
3.92929
4.66304
4-13342
4.89898
4.34788
5-I47I9
4-57321
5.40827
4.80998
5.68287
0.6
3-55622
4-96113
3-74097
5-21217
3-935o6
5.47624
4.13900
5-754QI
4-35329
6.04606
0.65
3.16122
5.22864
3-32545
5-49321
3-49799
5-77153
3.67927
6.06427
3.86976
6.37218
0.7
2.74674
546392
2.88943
5-74039
3-03934
6.03123
3.19686
6-337H
3-36237
6.65891
0-7S
2-3I53I
5-66550
2-43559
5-952i8
2.56196
6.25374
2.69474
6.57095
2.83425
6.90458
0.8
1. 86961
5-83215
1.96674
6.12727
2.06878
6.43770
2.17600
6.76424
2.28866
7.10769
0.85
1-41239
5.96287
I-48577
6.26458
1.56285
6.58199
1.64385
6.91583
1.72896
7.26697
0.9
0.94646
6.05680
o-99563
6.36327
1.04729
6.68567
1.10156
7.02478
1-15859
7.38146
o-95
0.47469
6.11339
0-49935
6.42273
0.52526
6.74814
0.55249
7.09042
0.58109
7-45043
1.0
0.00
6.13229
0.00
6.44259
0.00
6.76901
0.00
7-11234
0.00
7-47347
1.05
0.47469
6.11339
0-49935
6.42273
0.52526
6.74814
0.55249
7.09042
0.58109
7-45043
1.1
0.94646
6.05680
0.99563
6.36327
1.04729
6.68567
1.10156
7.02478
1-15859
7.38146
i-i5
1.41239
5.96287
I.48577
6.26458
1.56285
6.58199
1.64385
6.91583
1.72896
7.26697
1.2
1. 8696 1
5-832I5
1.96674
6.12727
2.06878
6.43770
2.17600
6.76424
2.28866
7.10769
1.25
2.31531
5-66550
2-43559
5.95218
2.56196
6-25374
2.69474
6.57095
2.83425
6.90458
i-3
2.74674
5-46392
2.88943
5-74039
3-03934
6.03123
3.19686
6.337H
336237
6.65891
i-3S
3.16122
5.22864
3-32545
5-49321
3-49799
5-77153
3.67927
6.06427
386976
6.37218
1.4
3-55622
4-96113
374097
5.21217
393506
5.47624
4.13900
5- 75401
4-35329
6.04606
i-4S
3.92929
4.66304
4-13342
4.89898
4.34788
5-I47I9
4.57321
5.40827
4.80998
5.68287
i-5
4.27814
4-336i9
450039
4-5556o
473389
4.78641
4-97923
5.02919
5.23702
5-28454
i-55
4.60062
3.98260
4-83961
4-18413
5.09071
4.39612
5-35454
4.61910
5-63177
4-85363
1.6
4.89472
3.60448
5.14900
3.78686
5-41615
3.97872
569685
4.18053
599179
4-39279
1.65
5-15865
3.20411
5.42664
3.36624
5.70819
3-5368o
6.00403
3-71619
6.31488
3.90488
i-7
5.39077
2.78401
5.67082
2.92488
5-96505
3.07306
6.27419
3.22894
6.59903
3.39288
1-75
5.58966
2-34673
5.88004
2.46547
6.18512
2-59039
6.50567
2.72178
6.84249
2.85997
1.8
5-75408
1.89498
6.05301
1.99087
6.36706
2.09174
6.69705
2.19784
7-04377
2.30943
1.85
588304
I-43I5S
6.18866
I-50399
6.50976
1. 58019
6.84713
1.66034
7.20163
1.74465
1.9
5-97572
0-95930
6.28615
1.00784
6.61231
1.05891
6.95500
1.11262
7.31508
1.16911
1-95
6.03155
0.481 13
6.34489
0.50548
6.67409
0.53109
7.01998
0.55803
7.38343
0.58636
2.0
6.05020
0.00
6.36451
0.00
6.69473
0.00
7.04169
0.00
7.40626
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (2.7 4- t'0.7) = 3.36237 4- i 6.65891.
sinh (2.5 4- i 1.25) - -2.31531 4- i 5.66550.
[52]
Table VII. HYPERBOLIC SINES, sinh (* + iq) = u + iv. Continued
x = 2.75
X = 2.8
x = 2.85
x 2.9
x = 2.95
7-7893S
0.00
8.19192
0.00
8.61497
0.00
9-05956
0.00
9.52681
O.00
0.05
7-76534
0.61616
8.16666
0.64750
8.58841
0.68046
9.03163
0.71512
9-49744
0.75I57
O.I
7-69345
1.22852
8.09106
1.29101
8.50891
I.35673
8.94802
1-42583
9.40952
1. 4985 1
o.is
7-57413
1-83331
7.96557
1.92656
8.37694
2.02463
8.80924.
2.12776
9.26358
2.23621
0.2
7.4081 1
2.42680
7.79098
2.55023
8.19332
2.68005
8.61616
2.81656
9.06053
2.96012
0.25
7.19642
3-00532
7-56834
3.15818
7-959 J 9
3-31894
8.36994
3.48800
8.80162
3.66578
o-3
6.94036
3-5653I
7.29905
3.74666
7.67599
3-93738
8.07213
4-13793
8.48845
4.34884
0.3S
6.64151
4-10333
6.98476
4.31204
7-34547
4-53153
7-72455
4.76236
8.12294
5.00509
0.4
6.30172
4.61604
6.62740
4-85083
6.96966
5-09775
7-32934
5-35742
7-70735
5-63049
0-4S
5-9 2 37
5.10030
6.22918
5-35972
6.55088
5-63254
6.88894
6.91945
7.24424
6.22116
o-5
5-50790
5-553"
5.79256
5-83556
6.09170
6.13261
6.40608
6.44498
6.73647
6.77348
0-5S
5-05878
5.97168
5.32022
6.27542
5-59498
6.59486
5-88371
6.93078
6.18717
7.28404
0.6
4-57847
6-35344
4-81509
6.67660
5-06375
7.01646
5-32508
7.37385
5.63048
7.74969
0.65
4.06993
6.69602
4.28026
7.03661
4-50131
7-39479
4-7336i
7.77146
4-97774
8.16757
0.7
3-53629
6.99732
3-71905
7.35323
3.91112
7.72754
4-II295
8.12115
4.32508
8.53508
0-7S
2.98086
7-25548
3-I349I
7.62452
3.29681
8.01263
3.46694
8.42078
3-64575
8.84998
0.8
2.40704
7.46891
2.53144
7.84881
2.66217
8.24834
2.79956
8.66850
2-94395
9.11031
0.85
1.81839
7.63629
1.91237
8.02470
2.01112
8.43318
2.11491
8.86275
2.22399
9-31447
0.9
1.21852
7-75659
1. 28150
8.15112
1.34768
8.56604
1-41723
9.00237
1.49032
9.46121
o-95
0.61115
7.82907
0.64273
8.22728
0.67592
8.64608
0.71081
9.08649
0.74747
9.54962
1.0
0.00
7-85328
0.00
8.25273
0.00
8.67281
0.00
9.11458
0.00
9-57915
1. 05
0.61115
7.82907
0.64273
8.22728
0.67592
8.64608
0.71081
9.08649
0.74747
9.54962
1.1
1. 21852
7-75659
1. 28150
8.15112
1.34768
8.56604
1-41723
9.00237
1.49032
9.46121
115
1.81839
7.63629
1.91237
8.02470
2.01112
8.43318
2.11491
8.86275
2.22399
9-3 J 447
1.2
2.40704
7.46891
2.53M4
7.84881
2.66217
8.24834
2.79956
8.66850
2-94395
9.1 103 1
1-25
2.98086
7-25548
3-I349I
7.62452
3.29681
8.01263
3.46694
8.42078
3-64575
8.84998
i-3
353629
6.99732
3.71905
7-35323
3.91112
7.72754
4.11295
8.12115
4.32508
8.53508
i-35
4.06993
6.69602
4.28026
7.03661
4-50131
7-39479
4.7336i
7.77146
4-97774
8.16757
1.4
4-57847
6-35344
4.81509
6.67660
5-06375
7.01646
5.32508
7-37385
5.63048
7.74969
i-4S
5.05878
5.97168
5-32022
6.27542
5-59498
6.59486
5-88371
6.93078
6.18717
7.28404
1-5
5-50790
5-553"
579256
S.83556
6.09170
6.13261
6.40608
6.44498
6.73647
6.77348
i-55
592307
5.10030
6.22918
5-35972
6.55088
5-632S4
6.88894
5-9I945
7.24424
6.22116
1.6
6.30172
4.61604
6.62740
4.85083
6.96966
5-09775
732934
5-35742
7-70735
5-63049
1.65
6.64151
4-I0333
6.98476
4.31204
7-34547
4-53153
7-72455
4.76236
8.12294
5.00509
i-7
6.94036
3-5653I
7.29905
3.74666
7.67599
3-93738
8.07213
4-13793
8.48845
4.34884
1-75
7.19642
3-00532
7-56834
3-15818
7-95919
3-31894
8.36994
3.48800
8.80162
3.66578
1.8
7.4081 1
2.42680
7.79098
2.55023
8.19332
2.68005
8.61616
2.81656
9.06053
2.96012
1. 8 S
7-57413
1-83331
7-96557
1.92656
8.37694
2.02463
8.80924
2.12776
9.26358
2.23621
1.9
7.69345
1.22852
8.09106
1.29101
8.50891
I.35673
8.94802
1-42583
9.40952
1. 4985 1
1.95
7.76534
0.61616
8.16666
0.64750
8.58841
0.68046
9.03163
0.71512
9.49744
o.75i57
2.0
7.78935
0.00
8.19192
0.00
8.61497
0.00
905956
0.00
9.52681
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (2.9 + i 0.9) = 1.41723 + * 9.00237.
sinh (2.8 4- * 1^4) = 4.81509 + i 6.67660.
[53]
Table VII. HYPERBOLIC SINES, sinh (x + iq) - u + iv. Continued
x = 3.0
x = 3.05
x = 3.10
x = 3-15
x = 3.20
0.0
10.01787
0.00
io.53399
0.00
11.07645
0.00
1 1. 6466 1
0.00
12.24588
0.00
0.05
9.98699
0.78990
10.50150
0.83020
11.04230
0.87258
11. 61070
0.91714
12.20810
0.96399
O.I
9.89454
1-57493
10.40430
1.65529
10.94010
1-73979
11.50320
1.82863
12.09510
1.92205
0.15
9.74108
2.35025
10.24290
2.47017
10.77040
2.59626
11.32480
2.72885
11.90750
2.86826
0.2
9-52757
3.11108
10.01840
3.26982
10.53430
3-43673
11.07660
3.61224
11.64650
3.79678
0.25
9-25531
3-85273
9.73216
4.04931
10.23330
4.25602
10.76010
4-47336
11.31370
4.70190
o-3
8.92599
4.57062
9.38586
4-80383
9.86919
5.04906
10.37720
5.30690
10.91120
5-578o2
o-3S
8.54164
5.26034
8.98171
5-52874
9.44423
5.81097
9.93036
6.10773
10.44130
6.41976
0.4
8.10463
5.91762
8.52218
6.21956
8.96104
6.53705
9.42230
6.87089
9.90712
7.22191
o.45
7.61765
6.53842
8.01011
6.87204
8.42260
7.22284
8.85615
7.59170
9.31184
7-97954
-5
7.08371
7.11891
7.44866
7.48215
7.83223
7.86409
8.23539
8.26570
8.65915
8.68797
-55
6.50609
7-6555I
6.84128
8.04612
7-I9358
8.45686
7-56387
8.88873
7-953o6
9.34284
0.6
5-88836
8.14491
6.19173
8.56049
6.51058
8-99749
6.84570
9-45697
7-19795
9.9401 r
0.65
5-23433
8.58409
5.50400
9.02209
5-78743
9.48264
6.08533
9.96690
6.39846
10.47610
0.7
4.54806
8.97035
4-78233
9.42805
5.02860
9-90933
5-28745
10.41540
5-55952
10.94750
0-7S
3-83368
9-30131
4-03119
9-77589
4.23878
10.27490
4.45696
10.79970
4.68630
1 1. 35 140
0.8
3-09569
9-57492
3-255i8
10.06350
3.42281
10.57720
3-599oo
11.11730
3.78419
11.68530
0.85
2.33863
9.78949
2.45911
10.28900
2-58575
10.81420
2.71885
11.36650
2.85874
11.94720
0.9
1-56714
9-94371
1.64788
10.45110
1.73274
10.98460
1.82193
"-54550
1.91568
12.13540
0-95
0.78599
10.03660
0.82649
10.54870
0.86905
11.08720
0.91378
11.65340
0.96080
12.24880
1.0
0.00
10.06766
0.00
10.58135
0.00
11.12150
0.00
11.68946
0.00
12.28665
1.05
0.78599
10.03660
0.82649
10.54870
0.86905
11.08720
0.91378
11.65340
0.96080
12.24880
1.1
1. 56714
9-94371
1.64788
10.45110
1-73274
10.98460
1. 82193
H-54550
1. 91568
12.13540
i-i5
2.33863
9.78949
2.45911
10.28900
2.58575
10.81420
2.71885
11.36650
2.85874
11.94720
1.2
3-09569
9-57492
3-25518
10.06350
3.42281
10.57720
3-59900
11.11730
3.78419
11.68530
1. 25
3.83368
9.30131
4.03119
9-77589
4-23878
10.27490
4.45696
10.79970
4.68630
1 1. 35 140
i-3
4.54806
8.97035
478233
9.42805
5.02860
9-90933
5.28745
10.41540
5-55952
10.94750
i-3S
5-23433
8.58409
5.50400
9.02209
5.78743
9.48264
6.08533
9.96690
6.39846
10.47610
1.4
5.88836
8.14491
6.19173
8.56049
6.51058
8.99749
6.84570
9-45697
7-19795
9.9401 1
i-45
6.50609
7-6555I
6.84128
8.04612
7.I9358
8.45686
7-56387
8.88873
7.95306
9.34284
i-5
708371
7.11891
7.44866
7.48215
7.83223
7.86409
8.23539
8.26570
8.65915
8.68797
i-55
761765
6.53842
8.01011
6.87204
8.42260
7.22284
8.85615
7.59170
9-3 1 1 84
7-97954
1.6
8.10463
5.91762
8.52218
6.21956
8.96104
6.53705
9.42230
6.87089
9.90712
7.22191
1.65
8.54164
5.26034
8.98171
5-52874
9.44423
5.81097
9-93036
6.10773
10.44130
6.41976
i-7
8.92599
4.57062
938586
4.80383
9.86919
5.04906
10.37720
5.30690
10.91120
5.57802
i-75
9-25531
3-85273
9.73216
4.04931
10.23330
4.25602
10.76010
4-47336
11.31370
4.70190
1.8
9-52757
3.11108
10.01840
3.26982
10.53430
3-43673
11.07660
3.61224
11.64650
3.79678
1.85
9.74108
2.35025
10.24290
2.47017
10.77040
2.596^6
11.32480
2.72885
11.90750
2.86826
1.9
9.89454
1-57493
10.40430
1.65529
10.94010
1-73979
11.50320
1.82863
12.09510
1.92205
1 -95
9.98699
0.78990
10.50150
0.83020
11.04230
0.87258
1 1. 61070
0.91714
12.20810
0.96399
2.0
10.01787
0.00
10.53399
0.00
11.07645
0.00
1 1. 6466 1
0.00
12.24588
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (3.0 + * Q-95) = 0.78599 + i 10.03660.
sinh (3.0 + * 1.05) = 0.78599 + i 10.03660.
[54]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
x = 3.25
0.0
12.87578
0.00
0.05
12.83610
1.01326
O.I
12.71726
2.02028
0.15
12.52002
3.01484
0.2
12.24560
3.99082
0.2s
11.89566
4.94218
o-3
11.47240
5.86309
o-3S
10.97841
6.74784
0.4
10.41673
7-59099
<M5
9.79082
8.38733
0.5
o-i455
9.13197
-55
8.36217
9.82031
0.6
7.56820
10.44810
0.65
6.72758
11.01147
0.7
5-84548
11.50695
-75
4-92 735
11.93150
0.8
3-97883
12.28247
0.85
3-579
12-55773
0.9
2.01422
12.75550
o-95
1.01022
12.87474
1.0
0.00
12.91456
1. 05
1. 01022
12.87474
1.1
2.01422
12.75556
i-i5
3-00579
12.55773
1.2
3-97883
12.28247
1-25
4-92735
11.93150
i-3
S-84548
11.50695
i-35
6.72758
11.01147
1.4
7.56820
10.44810
1 -45
8.36217
9.82031
i-5
9-10455
9.13197
i-55
9.79082
8.38733
1.6
10.41673
7-59099
1.65
10.97841
6.74784
i-7
11.47240
5.86309
i-7S
11.89566
4.94218
1.8
12.24560
3.99082
1.85
12.52002
3.01484
1.9
12.71726
2.02028
i-95
12.83610
1.01326
2.0
12.87578
0.00
x = 3.30
13-53788 0.00
13.49615 1.06507
13.37120 2.12356
13.16388 3.16897
12.87530 4.19483
12.50736 5.19485
12.06234 6.16381
11.54294 7-09279
10.95235 7-97905
10.29428 8.81610
9.57273 9.59881
8.79215 10.32233
7.95737 10.98222
7.07352 11.57440
6.14670 12.09520
5.18072 12.54145
4.18343 12.91035
3.16036 13.19970
2.11780 13.40764
1.06217 13.53290
0.00 13-57476
1.06217 13.53290
2.11780 13.40764
3.16036 13.19970
4.18343 12.91035
5.18072 12.54145
6.14670 12.09520
7.07352 11.57440
7-95737 10.98222
8.79215 10.32233
9-57273 9-5988i
10.29428 8.81610
10.95235 7.97905
11.54294 7-09279
12.06234 6.16381
12.50736 5-I9485
12.87530 4.19483
13.16388 3.16897
13.37120 2.12356
13.49615 1.06507
I3.53788 0.00
x = 3-35
14.23382 0.00
14.18950 1.11953
14.05851 2.23215
13.84054 3.33101
I3-537I7 4-40933
x = 3.40
14.96536 0.00
14.91923 1. 17679
14.78111 2.34632
14.55188 3.50139
14-23291 4.63487
i3-!5033
5-46075
13.82620
5-73977
12.68244
6-47795
I3-33423
6.80928
12.13633
7-45549
12.76006
7.83682
ii-5i54i
8.38705
12.10723
8.81604
10.82349
9.26691
n-37975
9.74090
10.06483
10.08964
10.58212
10.60570
9.24413
10.85016
9.71923
11.40512
8.36643
"54379
8.79642
12.13423
7-43715
12.16623
7.81938
12.78852
6.46202
12.71369
6.79414
I3-36397
5-44705
13.18275
5.72700
13.85702
4-39850
I3-57054
4-62455
14.26465
3.32282
13-87465
3-49359
14.58432
2.22666
14.09323
2.341 10
14.81410
1.11677
14.22498
1.17417
14.95250
0.00 14.26891
1.11677 14.22498
2.22666 14.09323
3.32282 13.87465
4-39850 13-57054
5.44705 13.18275
6.46202 12.71369
7-43715 12.16623
8.36643 11.54379
9.24413 10.85016
10.06483 10.08964
10.82349 9.26691
11.51541 8.38705
12.13633 7-45549
12.68244 6.47795
13-15033 5-46075
I3.537I7 4-40933
13.84054 3.33101
14.05851 2.23215
14.18950 1.11953
14.23382 0.00
0.00 14.99874
1.17417 I4-Q525Q
2.34110 14.81410
3-49359 I4-58432
4.62455 14.26465
5.72700 13.85702
6.79414 I3-36397
7.81938 12.78852
8.79642 12.13423
9.71923 11.40512
10.58212 10.60570
H-37975 9-74090
12.10723 8.81604
12.76006 7.83682
I3-33423 6.80928
13.82620 5.73977
14.23291 4-63487
14.55188 3.50139
14.78111 2.34632
14.91923 1. 17679
14.96536 0.00
x = 3-45
I5-73432 0.00
15.68581 1.23699
15.54061 2.46636
15.29959 3.68053
14.96423 4.87198
14.53662 6.03341
14.01940 7-15765
13.41572 8.23775
12.72933 9.26706
11.96447 10.23924
11. 12585 11. 14830
10.21863 1 1. 98861
9.24840 12 75501
8.22116 13.44278
7.14324 14.04764
6.02127 14.56595
4.86217 14.99442
3.6731 1 15.33045
2.46139 15.57196
1.23450 15.71746
0.00 15.76607
1.23450 15.71746
2.46139 15-57196
3.67311 1533045
4.86217 14.99442
6.02127 14-56595
7.14324 14.04764
8.22116 13.44278
9.24840 12.75501
10.21863 n-c
11. 12585 11. 14830
11.96447 10.23924
12.72933 9.26706
13.41572 8.23775
14.01940 7-I5765
14.53662 6.03341
14.96423 4.87198
15.29959 3-68053
15.54061 2.46636
15.68581 1.23699
15-73432 0.00
Note.
Negative questions are in heavy type.
Examples, sinh (3.40 + j o) = 14.96536 + i o.
sinh (3.45 + i 1.45) = 10.21863 + i 11. 98861.
[55]
Table VII. HYPERBOLIC SINES, sinh (* + iq) = u + iv. Continued
3-5
* = 3-55
x 3.60
x = 3.65
x = 3.70
0.0
16.54263
0.00
17.39230
0.00
18.28546
0.00
19.22434
0.00
20.21129
O.00
0.05
16.49163
1.30029
17.33870
1.36684
18.22900
1.43680
19.16506
1.51036
20.14900
1.58770
O.I
16.33896
2.59256
17.17817
2.72525
18.06033
2.86475
18.98765
3.01142
19.96246
3-16561
0.15
16.08555
3-86885
16.91175
4.06686
17.78022
4-27503
18.69316
4.49390
19.65290
4.72401
0.2
I5-73300
5.12129
16.54105
5-38339
17.39050
5-65896
18.28342
5.94868
19.22208
6.25327
0.2s
15.28340
6.34215
16.06840
6.66674
16.89356
7.00800
17.76096
7.36678
18.67280
7-74399
-3
14.73960
7-5239 1
15.49665
7.90898
16.29246
8.31383
17.12900
8.73946
18.00840
9.18696
-35
14.10490
8.65928
14.82933
9.10246
15.59090
9.56840
16.39143
[0.05827
17.23295
10.57330
0.4
13-38330
9.74126
14.07066
10.23982
14.79326
10.76400
I5-5528I
ti-3 I SQ5
16.35127
11.89444
o.45
12.57910
10.76320
13.22520
1 1. 3 1405
13.90436
11.89320
14.61830
[2.50208
15.36878
13.14223
-5
11.69740
11. 71820
12.29820
12.31852
12.92978
12.94910
I3.59365
[3.61203
14-29155
14.30902
0-5S
io.74357
12.60210
11.29540
13.24705
n-87545
I3-925I5
12.48520
[4.63806
13.12620
15.38760
0.6
9.72361
13.40770
10.22293
14.09390
10.74789
I4-8I535
11.29972
[5-57383
11.87990
16.37127
0.65
8.64360
14.13065
9.08745
14.85386
9-55412
15.61421
10.04469
[6.41360
10.56037
17.25404
0.7
7.51020
14.76650
7-89594
15.52225
8.30143
16.31680
8.72766
[7.15216
9-*7573
18.03040
0-7S
6.33059
15.31130
6.65574
16.09492
6-99754
16.91880
7-35683
[7.78497
7-73453
18.69565
0.8
5-IH95
15.76170
5-37451
16.56840
5-65052
17.41650
5.94065
[8.30814
6.24563
19.24560
0.85
3.86180
16.11491
4.06015
16.93970
4.26865
17.80680
4.48783
[8.71843
4.71823
19.67690
0.9
2.58783
16.36878
2.72075
17.20653
2.86047
18.08732
3-oo735
[9.01331
3-16174
19.98688
o-95
1.29792
16.52173
1.36458
17.36731
1.43466
18.25632
1.50832
[9.19100
I-58576
20.17362
1.0
0.00
16.57282
0.00
17.42102
0.00
18.31278
0.00
[9-25033
0.00
20.23601
1.05
1.29792
16.52173
1.36458
17.36731
1.43466
18.25632
1.50832
[9.19100
I-58576
20.17362
1.1
2.58783
16.36878
2.72075
17.20653
2.86047
18.08732
3-00735
[9.01331
3-16174
19.98688
"S
3.86180
16.11491
4.06015
16.93970
4.26865
17.80680
4.48783
[8.71843
4-71823
19.67690
1.2
5.1119S
15.76170
5-37451
16.56840
5-65052
17.41650
5-94065
[8.30814
6.24563
19.24560
1.25
6.33059
i5-3"3o
6.65574
16.09492
6-99754
16.91880
7.35683 l
[7.78497
7-73453
18.69565
1-3
7.51020
14.76650
7.89594
15-52225
8.30143
16.31680
8.72766
[7.15216
9-17573
18.03040
1 -35
8.64360
14.13065
9.08745
14.85386
9-55412
15.61421
10.04469
6.41360
10.56037
17.25404
1.4
972361
13.40770
10.22293
14.09390
10.74789
I4-8I535
11.29972 i
5-57383
11.87990
16.37127
J 45
io.74357
12.60210
11.29540
13.24705
11.87545
I3-925I5
12.48520 ]
4.63806
13.12620
15.38760
i-S
11.69740
11. 71820
12.29820
12.31852
12.92978
12.94910
13-59365 l
3.61203
14.29155
14.30902
i-55
12.57910
10.76320
13.22520
1 1. 3 1405
13.90436
11.89320
14.61830 i
2.50208
15.36878
13.14223
1.6
1338330
9.74126
14.07066
10.23982
14.79326
10.76400
15.55281 i
1-31505
16.35127
11.89444
1.65
14.10490
8.65928
14.82933
9.10246
15.59090
9.56840
16.39143 'l
0.05827
I7-23295
,10.57330
i-7
14.73960
7-5239 1
15.49665
7.90898
16.29246
8.31383
17.12900
8.73946
18.00840
9.18696
i-75
15.28340
6.34215
16.06840
6.66674
16.89356
7.00800
17.76096
7.36678
18.67280
7-74399
1.8
i5-733oo
5-12129
16.54105
5-38339
I7.39050
5.65896
18.28342
5.94868
19.22208
6.25327
1.85
16.08555
3-86885
16.91175
4.06686
17.78022
4-27503
18.69316
4.49390
19.65290
4.72401
1.9
16.33896
2.59256
17.17817
2.72525
18.06033
2.86475
18.98765
3.01142
19.96246
3-16561
i-95
16.49163
1.30029
17.33870
1.36684
18.22900
1.43680
19.16506
1. 51036
20.14900
1.58770
2.0
16.54263
0.00
I7-39230
0.00
18.28546
0.00
19.22434
0.00
20.21129
0.00
Note. Negative quantities are in heavy type.
Examples, sinh (3.70 +
i Q-5) = I4-29I55 +
i 14.30902.
sinh (3.70 4- i 1^) = 14.29155 + i 14.30902.
[56]
Table VII. HYPERBOLIC SINES, sinh (x + iq) = u + iv. Continued
* = 3-75
o.o
21.24878
0.00
0.05
21.18327
1.66900
O.I
20.98716
3.32772
0.15
20.66167
4.96592
0.2
20.20879
6.57350
0.2s
19.63131
8.14055
o-3
18.93280
9.65741
o-3S
18.11756
11.11473
0.4
17.19062
12.50353
o.45
16.15770
13.81524
0.5
15.02516
15.04177
o-55
13.79998
16.17556
0.6
12.48971
17.20963
0.65
11. 10246
18.13760
0.7
9.64674
18.95373
o.75
8.^3156
19.65301
0.8
6.56624
20.23113
0.85
4.96043
20.68452
0.9
3-32404
21.01038
O.05
1.66716
21.20670
1.0
0.00
21.27230
1. 05
1.66716
21.20670
1.1
3-32404
21.01038
i-i5
4.96043
20.68452
1.2
6.56624
20.23113
1-25
8.13156
19.65301
i-3
9.64674
18.95373
1-35
11. 10246
18.13760
1.4
12.48971
17.20963
i-4S
I3-79998
16.17556
i-5
15.02516
15.04177
1-55
16.15770
13.81524
1.6
17.19062
12.50353
1.65
18.11756
11.11473
i-7
18.93280
9.65741
i-75.
19.63131
8.14055
1.8
20.20879
6.57350
1.85
20.66167
4.96592
1.9
20.98716
3.32772
i-95
21.18327
1.66900
2.0 21.24878 0.00
x = 3.80
22.33941 0.00
22.27052 1.75448
22.06437 3.49815
21.72216 5.22025
21.24603 6.91017
20.63891 8.55748
19.90455 10.15203
19.04746 11.68400
18.07296 13.14392
16.98701 14.52281
15.79634 15.81216
14.50828 17.00402
13.13076 18.09105
11.67230 19.06655
10.14188 19.92448
8.54892 20.65958
6.96325 21.26731
5.21503 21.74391
3.49465 22.08646
1.75273 22.29283
0.00 22.36178
1.75273 22.29283
3.49465 22.08646
5.21503 21.74391
6.90325 21.26731
8.54892 20.65958
10.14188 19.92448
11.67230 19.06655
13.13076 18.09105
14.50828 17.00402
15.79634 15-81216
16.98701 14.52281
18.07296 13.14392
19.04746 11.68400
19.90455 10.15203
20.63891 8.55748
21.24603 6.91017
21.72216 5.22025
22.06437 3-49815
22.27052 1.75448
22.33941 0.00
x = 3-85
23.48589 0.00
23.41348 1.84435
23.19673 3.67733
22.83696 5.48764
22.33640 7.2641 1
21.69813 8.99580
20.92608 10.67203
20.02501 12.28246
19.00048 13.81716
17.85880 15.26668
16.60702 16.62208
15.25286 17.87500
13.80465 19.01770
12.27134 20.04315
10.66233 20.94503
8.98766 21.71778
7.25754 22.35664
5.48267 22.85766
3.67400 23.21775
1.84268 23.43470
0.00 23.50717
1.84268 23.43470
3.67400 23.21775
5.48267 22.85766
7.25754 22.35664
8.98766 21.71778
10.66233 20.94503
12.27134 20.04315
13.80465 19.01770
15.25286 17.87500
16.60702 16.62208
17.85880 15.26668
19.00048 13.81716
20.02501 12.28246
20.92608 10.67203
21.69813 8.99580
22.33640 7.26411
22.83696 5.48764
23.19673 3-67733
23.41348 1.84435
x = 3.90
24.69110 0.00
24.61500 1.93883
24.38710 3.86571
24.00888 5.76875
23.48262 7.63623
22.81160 9.45662
21.99993 11.21871
21.05272 12.91164
19.97556 14.52497
18.77526 16.04874
17.45924 17-47355
16.03558 18.79065
14.51307 19.99190
12.90106 21.06988
11.20952 22.01797
9.44887 22.83030
7.62997 23.50188
5.76402 24.02856
3.86254 24.40710
1.93724 24.63516
0.00 24.71135
1.93724 24.63516
3.86254 24.40710
5.76402 24.02856
7.62997 23.50188
9.44887 22.83030
11.20952 22.01797
12.90106 21.06988
14.51307 19.99190
16.03558 18.79065
17.45924 17-47355
18.77526 16.04874
I9.97556 14-52497
21.05272 12.91164
21.99993 11.21871
22.81160 9.45662
23.48262 7.63623
24.00888 5.76875
24.38710 3-86571
24.61500 1.93883
* = 3-95
25.95806 0.00
25.87805 2.03816
25.63849 4-06375
25.24084 6.06429
24.68760 8.02744
23.98212 9.94109
23.12881 11.79366
22.13290 13.57315
21.00052 15.26910
19.73867 16.87098
18.35512 18.36873
16.85842 19.75331
x 5- 2 5776 21.01610
13-56305 22.14931
11.78474 23.14597
9-93373 23.99991
8.02149 24.70590
6.05979 25.25957
4.06074 25.65749
2.03665 25.89724
0.00 25.97731
2.03665 25.89724
4.06074 25.65749
6.05979 25.25957
8.02149 24.70590
9-93373 23.99991
II.78474 23.14597
13.56305 22.14931
15.25776 21.01610
16.85842 I9.7533 1
18.35512 18.36873
19.73867 16.87098
21.00052 15.26910
22.13290 i3-573 I S
23.12881 11.79366
23.98212 9.94109
24.68760 8.02744
25.24084 6.06429
25.63849 4-06375
25.87805 2.03816
23.48589 0.00 24.69110 0.00 25.95806 0.00
Note. Negative quantities are in heavy type.
Examples, sinh (3.90 + i 0.75 ) = 9.44887 + i 22.83030.
sinh (3.95 + i 1.95) = -25.87805 + i 2.03816.
[57]
Table VIII. HYPERBOLIC COSINES, cosh (as + iq) = u + iv
0.05
0.15
1. 0000
0.00
1.00125
0.00
1 .00500
0.00
1.01127
0.00
1.02007
0.00
0.05
0.99692
0.00
0.99816
0.00392
1.00191
0.00786
1.00815
0.01181
1.01692
0.01580
O.I
0.98769
0.00
0.98892
0.00783
0.99263
0.01567
0.99882
0.02355
1.00751
0.03150
0.15
0.97237
0.00
0.97385
0.01168
0.97724
0.02338
0.98333
0.03515
0.99188
0.04700
0.2
0.95106
0.00
0.95225
0.01546
0.95582
0.03095
0.96178
0.04653
0.97014
0.06222
0.25
0.92388
0.00
0.92503
0.01914
0.92850
0.03833
0.93429
0.05762
0.94242
0.07705
0.3
0.89101
0.00
0.89208
0.02271
0.89547
0.04547
0.90105
0.06835
0.90889
0.09141'
0.3s
0.85264
0.00
0.85367
0.02614
0.85691
0.05234
0.86225
0.07867
0.86975
0.10520
0.4
0.80902
0.00
0.81000
0.02940
0.81307
0.05888
0.81814
0.08850
0.82525
0.1 1834
0.4s
0.76041
0.00
0.76133
0.03249
0.76421
0.06505
0.76898
0.09778
0.77567
0.13076
0.5
0.70711
0.00
0.70796
0.03537
0.71065
0.07083
0.71508
0.10646
0.72130
0.14237
0.55
0.64945
0.00
0.65023
0.03804
0.65270
0.07617
0.65677
0.1 1449
0.66248
0.15310
0.6
0.58779
0.00
0.58850
0.04047
0.59027
0.08104
0.59441
0.12181
0.59958
0.16288
0.6s
0.52250
0.00
0.52313
0.04265
0.52511
0.08541
0.52839
0.12838
0.53298
0.17167
0.7
Q-45399
0.00
0.45439
0.04457
0.45626
0.08925
0.4591 1
0.13415
0.46310
0.17939
0.75
0.38268
0.00
0.38316
0.04621
0.38460
0.09254
0.38700
0.13910
0.39036
0.1 8601
0.8
0.30902
0.00
0.30940
0.04757
0.31056
0.09526
0.31250
0.14319
0.31522
0.1 9 148
0.8s
0.23345
0.00
0.23374
0.04864
0.23461
0.09740
0.23608
0.14640
0.23813
O.I9577
0.9
0.15643
0.00
0.15663
0.04941
0:15722
0.09893
0.15820
0.14871
0.15957
0.19886
o-95
0.07846
0.00
0.07856
0.04987
0.07885
0.09986
0.07934
0.15010
0.08003
0.20072
1.0
0.00
0.00
0.00
0.05002
0.00
0.10017
0.00
0.15056
0.00
0.20134
1.05
0.07846
0.00
0.07856
0.04987
0.07885
0.09986
0.07934
0.15010
0.08003
0.20072
1.1
0.15643
0.00
0.15663
0.04941
0.15722
0.09893
0.15820
0.14871
0.15957
0.19886
t.%s
0.23345
0.00
0.23374
0.04864
0.23461
0.09740
0.23608
0.14640
0.23813
0.19577
1.2
0.30902
0.00
0.30940
0.04757
0.31056
0.09526
0.31250
0.143 19
0.31522
0.19148
1.25
0.38268
0.00
0.38316
0.04621
0.38460
0.09254
0.38700
0.13910
0.39036
0.18601
i-3
0.45399
0.00
o.45439
0.04457
0.45626
0.08925
0.4591 1
0.13415
0.46310
O.I7939
i-35
0.52250
0.00
0.52313
0.04265
0.52511
0.08541
0.52839
0.12838
0.53298
0.17167
1.4
0.58779
0.00
0.58850
0.04047
0.59027
0.08104
0.59441
0.12181
0.59958
0.16288
1 -45
0.64945
0.00
0.65023
0.03804
0.65270
0.07617
0.65677
0.1 1449
0.66248
0.15310
i-5
0.7071 1
0.00
0.70796
0.03537
0.71065
0.07083
0.71508
0.10646
0.72130
0.14237
1-55
0.76041
0.00
0.76133
0.03249
0.76421
0.06505
0.76898
0.09778
0.77567
0.13076
1.6
0.80902
0.00
0.81000
0.02940
0.81307
0.05888
0.81814
0.08850
0.82525
0.1 1 834
1.6S
0.85264
0.00
0.85367
0.02614
0.85691
0.05234
0.86225
0.07867
0.86975
0.10520
i-7
0.89101
O.OJ
0.89208
0.02271
0.89547
0.04547
0.90105
0.06835
0.90889
0.09 1 41
i-75
0.92388
0.00
0.92503
0.01914
0.92850
0.03833
0.93429
0.05762
0.94242
0.07705
1.8
0.95106
0.00
0.95225
0.01546
0.95582
0.03095
0.96178
0.04653
0.97014
0.06222
1.85
0.97237
0.00
0.97385
0.01168
0.97724
0.02338
0.98333
0.03515
0.99188
0.04700
1.9
0.98769
0.00
0.98892
0.00783
0.99263
0.01567
0.99882
0.02355
1.00751
0.03150
1 -95
0.99692
0.00
0.99816
0.00392
1.00191
0.00786
1. 00815
0.01181
1. 01692
0.01580
2.0
1. 0000
0.00
1. 00125
0.00
1.00500
0.00
1.01127
0.00
1.02007
0.00
Note. Negative quantities are in heavy type.
Examples, cosh (0 + i 0.75) = c
'.38268 +
i 0.
cosh (0.2 + i 1.5) = 0.72130 + i 0.14237
[58]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
0.25
x = 0.3
x = 0.35
x = 0.4
x = 0.45
1.03 141
0.00
I -04534
0.00
1. 06 1 88
0.00
1.08107
0.00
1. 10297
0.00
0.05
1.02823
0.01982
I.O42 1 2
0.02389
1.05860
0.02803
1.07774
0.03223
1.09957
0.03651
O.I
1.01871
0.03952
I.O3247
0.04764
1.04880
0.05588
1.06776
0.06426
1.08939
0.07280
0.15
1.00292
0.05897
I.O1646
0.07109
1-03254
0.08338
1. 05 1 20
0.09589
1.07250
0.10863
0.2
0.98093
0.07806
O.99418
0.09410
1.00991
0.11038
1.02816
0.12693
1 .04899
0.14380
0.25
0.95290
0.09667
O.96577
0.1 1654
0.98105
0.13669
0.99S78
0.15719
1.01901
0.17808
o-3
0.91900
0.1 1468
O.93I4O
0.13825
0.94614
0.16216
0.96324
0.18648
0.98275
0.21126
o-35
0.87942
0.13 199
O.89I3O
o.i59n
0.90540
0.18663
0.92177
0.21462
0.94044
0.24314
0.4
0.83443
0.14848
O.8457O
0.17899
0.85908
0.20995
0.87461
0.24143
0.89232
0.27352
o-45
0.78429
0.16406
O.79488
0.19777
0.80746
0.23198
0.82206
0.26676
0.83871
0.30222
-5
0.72932
0.17862
O.73917
0.2I533
0.75086
0.25257
0.76443
0.29045
0.77992
0.32905
o-55
0.66985
0.19208
O.67889
0.23156
0.68964
0.27161
0.70210
0.31234
0.71632
0-35385
0.6
0.60625
0.20437
O.61444
0.24636
0.62416
0.28897
0.63544
0.33231
0.64831
0.37647
0.65
0.53891
0.21539
O.54619
0.25965
0.55483
0.30455
0.56486
0.35022
0.57630
0.39677
0.7
0.46825
0.22508
0.47457
0.27133
0.48208
0.31826
0.49080
0.36598
0.50074
0.41462
o.75
0.39471
0.23338
O.4OOO3
0.28134
0.40636
0.33000
0.41371
o.37949
0.42209
0.42992
0.8
0.31872
0.24025
0.32303
0.28962
0.32814
o.3397i
0.33407
0.39065
0.34084
0.44257
0.85
0.24078
0.24563
O.244O3
0.2961 1
0.24789
o.34732
0.25237
o.3994o
0.25748
0.45249
0.9
0.16135
0.24950
O.16353
0.30077
0.16611
0.35279
0.16912
0.40570
0.17254
0.45961
0-9S
0.08092
0.25183
0.08202
O.30358
0.08331
0.35609
0.08482
0.40949
0.08654
0.46391
1.0
0.00
0.25261
O.OO
0.30452
0.00
0.35719
0.00
0.41075
0.00
0.46534
1.05
0.08092
0.25183
0.08202
0.30358
0.08331
0.35609
0.08482
0.40949
0.08654
0.46391
i.r
0.16135
0.24950
O.I6353
0.30077
0.16611
0.35279
0.16912
0.40570
0.17254
0.45961
i-i5
0.24078
0.24563
O.24403
0.29611
0.24789
o.34732
0.25237
0.39940
0.25748
0.45249
1.2
0.31872
0.24025
0.32303
0.28962
0.32814
o.3397i
0.33407
0.39065
0.34084
0.44257
1.25
0.39471
0.23338
O.4OOO3
0.28134
0.40636
0.33000
0.41371
o.37949
0.42209
0.42992
i-3
0.46825
0.22508
0.47457
0.27133
0.48208
0.31826
0.49080
0.36598
0.50074
0.41462
1 -35
0.53891
0.21539
O.54619
0.25965
0.55483
0.30455
0.56486
0.35022
0.57630
0.39677
1.4
0.60625
0.20437
O.61444
0.24636
0.62416
0.28897
0.63544
0.33231
0.64831
0.37647
i-45
0.66985
0.19208
O.67889
0.23156
0.68964
0.27161
0.70210
0.31234
0.71632
0.35385
i-5
0.72932
0.17862
O.73917
0.21533
0.75086
0.25257
0.76443
0.20945
0.77992
0.32905
1-55
0.78429
0.16406
O.79488
0.19777
0.80746
0.23198
0.82206
0.26676
0.83871
0.30222
1.6
0.83443
0.14848
O.8457O
0.17899
0.85908
0.20995
0.87461
0.24143
0.89232
0.27352
1.6S
0.87942
0.13199
O.8913O
0.15911
0.90540
0.18663
0.92177
0.21462
0.94044
0.24314
i-7
0.91900
0.1 1468
O.9314O
O.13825
0.94614
0.16216
0.96324
0.18648
0.98275
0.21126
i-75
0.95290
0.09667
0.96577
0.11654
0.98105
0.13669
0.99878
0.15719
1.01901
0.17808
1.8
0.98093
0.07806
O.99418
0.09410
1. 0099 1
0.1 1038
1. 02816
0.12693
1.04899
0.14380
1.85
1.00292
0.05897
1. 01 646
0.07109
1.03254
0.08338
1. 05120
0.09589
1.07250
0.10863
1.9
1.01871
0.03952
I.O3247
0.04764
1.04880
0.05588
1.06776
0.06426
1.08939
0.07280
i-9S
1.02823
0.01982
1. 04212
0.02389
1.05860
0.02803
1.07774
0.03223
1.09957
0.03651
2.0
1.03141
0.00
1.04534
0.00
1. 06188
0.00
1.08107
0.00
1. 10297
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (0.3 + i 0.9) = 0.16353 + i 0.30077;
cosh (0.45 -f- i 1.7) = 0.98275 + * 0.21126.
[59]
Table VIII. HYPERBOLIC COSINES, cosh (* + iq) = u + iv. Continued
x = 0.5
x = 0.55
x = 0.6
x = 0.65
x = 0.7
1. 12763
0.00
1.15510
0.00
1. 18547
0.00
1. 21879
0.00
I-255I7
O.00
0.05
1.12415
0.04088
I-I5I54
0.04536
1.18181
0.04995
1. 21504
0.05467
1. 25130
0.05952
O.I
I-H374
0.08152
1. 14088
0.09044
1. 17087
0.09959
1.20379
0.10900
1.23972
0.11867
0.15
1.09647
0.12165
1.12319
0.13497
1.15271
0.14862
1.18512
0.16265
1.22049
0.17709
0.2
1.07244
0.1 6 103
1.09857
0.17866
1. 12744
0.19674
1.15912
0.21531
I-I9374
0.23442
0.25
1.04179
0.19942
1.06717
0.22125
1.09523
0.24364
1. 12602
0.26663
1. 15962
0.29030
-3
1.00472
0.23657
1.02920
0.26248
1.05626
0.28904
1.08595
0.31632
1.11836
0.34439
o.35
0.96146
0.27227
0.98489
0.30208
1.01078
0.33265
1.03919
0.36405
1.07021
0.39636
0.4
0.91227
0.30629
o.9345o
o.339 8 3
0.95906
0.37422
0.98602
0.40954
1 -OI545
0.44589
o.4S
0.85745
0.33842
0.87835
o.37548
0.90144
0.41347
0.92678
0.45250
0.95444
0.49266
-5
0-7973S
0.36847
0.81678
0.40882
0.83825
0.45018
0.86182
0.49268
0.88754
0.53640
o.55
0.73233
0.39624
0.75018
0.43963
0.76990
0.48412
0.79154
0.52981
0.81517
0.57683
0.6
0.66280
0.42158
0.67895
0.46773
0.69680
0.51506
0.71639
0.56368
o.73777
0.61371
0.65
0.58918
0.44431
0.60354
0.49296
0.61940
0.54284
0.63682
0.59408
0.65582
0.64680
0.7
0.51 193
0.46430
0.52441
0.51514
0.53819
0.56726
0.55332
0.62081
0.56984
0.67590
0-7S
0.43152
0.48143
0.44204
0.53414
0.45366
0.58819
0.46641
0.64371
0.48033
0.70084
0.8
0.34846
o.49559
o.3569S
0.54986
0.36633
0.60549
0.37663
0.66265
0.38787
0.72146
0.85
0.26324
0.50670
0.26965
0.56218
0.27674
0.61906
0.28452
0.67750
0.29301
0.73763
0.9
0.17640
0.51468
0.18070
0.57103
0.18545
0.62882
0.19066
0.68817
0.19635
0.74925
-95
0.08847
0.51949
0.09063
0.57637
0.09301
0.63469
0.09563
0.69460
0.09848
0.75625
1.0
0.00
0.52110
0.00
0.57815
0.00
0.63665
0.00
0.69675
0.00
0.75858
1.05
0.08847
0.51949
0.09063
0.57637
0.09301
0.63469
0.09563
0.69460
0.09848
0.75625
1.1
0.17640
0.51468
0.18070
0.57103
0.18545
0.62882
0.19066
0.68817
0.19635
0.74925
i-i5
0.26324
0.50670
0.26965
0.56218
0.27674
0.61906
0.28452
0.67750
0.29301
.0.73763
1.2
0.34846
0-49559
0.3569S
0.54986
0.36633
0.60549
0.37663
0.66265
0.38787
0.72146
1-25
0.43152
0.48143
0.44204
0.534H
0.45366
0.58819
0.46641
0.64371
0.48033
0.70084
i-3
0.51 193
0.46430
0.52441
0.51514
0.53819
0.56726
0-5S332
0.62081
0.56984
0.67590
1-35
0.58918
0.44431
0.60354
0.49296
0.61940
0.54284
0.63682
0.59408
0.65582
0.64680
1.4
0.66280
0.42158
0.67895
0.46773
0.69680
0.51506
0.71639
0.56368
0-73777
0.61371
1 45
0.73233
0.39624
0.75018
0.43963
0.76990
0.48412
0.79154
0.52981
0.81517
0.57683
i-5
0.79735
0.36847
0.81678
0.40882
0.83825
0.45018
0.86182
0.49268
0.88754
0.53640
i-55
0.8574S
0.33842
0.87835
0.37548
0.90144
0.41347
0.92678
0.45250
0.95444
0.49266
1.6
0.91227
0.30629
o.9345o
0-33983
0.95906
0.37422
0.98602
0.40954
1.01545
0.44589
1.65
0.96146
0.27227
0.98489
0.30208
1.01078
0.33265
1.03919
0.36405
1. 07021
0.39636
i-7
1.00472
0.23657
1.02920
0.26248
1.05626
0.28904
1.08595
0.31632
1.11836
0-34439
i-75
1.04179
0.19942
1. 067 1 7
0.22125
1.09523
0.24364
1. 12602
0.26663
1. 1 5962
0.29030
1.8
1.07244
0.16103
1.09857
0.17866
1. 12744
0.19674
1.15912
0.21531
I-I9374
0.23442
1.8S
1.09647
0.12165
1.12319
O.I3497
1.15271
0.14862
1.18512
0.16265
1.22049
0.17709
1.9
I.H374
0.08152
1. 14088
0.09044
1. 17087
0.09959
1.20379
0.10900
1.23972
0.1 1867
i-95
1.12415
0.04088
i-i5i54
0.04536
1.18181
0.04995
1. 21504
0.05467
1. 25130
0.05952
2.0
1. 12763
0.00
1.15510
0.00
1. 1 8547
0.00
1. 21879
0.00
I.25517
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (0.6 + * 0.95) = 0.09301 + i 0.63469.
cosh (0.6 + i 1.05) = 0.09301 + i 0.63469.
[60]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
x - 0.75
x - 0.8
= 0.85
x = 0.9
x = 0.95
1.29468 0.00
1-33743
0.00
I.38353
0.00
I-43309
0.00
I.48623
0.00
0.05
1.29069 0.06452
I-3333I
0.06968
1.37927
0.07502
1.42867
0.08054
I.48164
0.08627
O.I
1.27874 0.12864
1.32097
0.13893
1.36650
0.14957
I-4I544
0.16058
1.46793
0.17200
0.15
1.25891 0.19197
1.30048
0.20732
I-34530
0.22320
1-39349
0.23964
I-445I6
0.25667
0.2
1. 23132 0.25411
1. 27198
0.27444
1.31582
0.29546
1.36294
0.31721
I.41348
c.33976
0.25
1.19613 0.31469
1-23563
0.33986
1.27822
0.36589
1.32400
0.39283
I.37309
0.42076
0.3
1. 15356 0.37332
1.19166
0.40319
1.23274
0.43407
1.27689
0.46603
1-32425
0.49916
o-3S
1. 10390 0.42966
1-14035
0.46403
1. 17965
o.49957
1. 22194
0-53635
I.26722
0.57448
0.4
1.04742 0.48335
1.08201
0.52202
1.11930
0.56199
I-I5939
0.60337
I.20238
0.64626
o.4S
0.98449 0.53405
1.01700
0.57678
1.05205
0.62095
1.08973
0.66667
I.13013
0.71406
o-5
0.91548 0.58147
0.94571
0.62799
0.97830
0.67608
I-OI334
0.72586
1.05092
o.77745
o.55
0.84083 0.62529
0.86859
0.67532
0.89853
0.72704
0.93071
0.78057
0.96523
0.83605
0.6
0.76100 0.66527
0.78613
0.71849
0.81322
o.7735i
0.84235
0.83047
0.87358
0.88950
0.65
0.67647 0.701 14
0.69881
0.75724
0.72290
0.81522
0.74879
0.87525
0.77655
0-93747
0.7
0.58777 0.73269
0.60718
0.79131
0.62811
0.85191
0.65061
0.91463
0.67473
0.97965
0-7S
o.49545 0.75972
0.51182
0.82050
0.52945
0.88334
0.54842
0.94838
0.56875
1.01579
0.8
0.40008 0.78207
0.41329
0.84464
0.42753
0.90932
0.44285
0.97628
0.45927
1.04567
0.85
0.30224 0.79960
0.31222
0.86357
0.32298
0.92970
0-33455
0.99816
0.34695
1. 069 1 1
0.9
0.20253 0.81219
0.20922
0.87717
0.21643
o.94435
0.22418
1.01388
0.23250
1.08595
o-95
0.10158 0.81978
0.10493
0.88537
0.10855
o-953i7
0.11244
1-02335
0.11661
1. 096 10
1.0
0.00 0.82232
0.00
0.8881 1
0.00
0.95612
0.00
1.02652
0.00
1.09948
1.05
0.10158 0.81978
0.10493
0.88537
0.10855
o-953i7
0.11244
1-02335
0.11661
1. 096 10
1.1
0.20253 0.81219
0.20922
0.87717
0.21643
o.94435
0.22418
1.01388
0.23250
1.08595
*.J
0.30224 0.79960
0.31222
0.86357
0.32298
0.92970
0.33455
0.99816
0.34695
1. 069 1 1
1.2
0.40008 0.78207
0.41329
0.84464
0.42753
0.90932
0.44285
0.97628
0.45927
1.04567
i-2S
0.49545 0.75972
0.51182
0.82050
0.52945
0.88334
0.54842
0.94838
0.56875
1.01579
i-3
0.58777 0.73269
0.60718
0.79131
0.6281 1
0.85191
0.65061
0.91463
0.67473
0.97965
i-35
0.67647 0.701 14
0.69881
0.75724
0.72290
0.81522
0.74879
0.87525
0.77655
C93747
1.4
0.76100 0.66527
0.78613
0.71849
0.81322
o.7735i
0.84235
0.83047
0.87358
0.88950
i-45
0.84083 0.62529
0.86859
0.67532
0.89853
0.72704
0.93071
0.78057
0.96523
0.83605
i-5
0.91548 0.58147
0.94571
0.62799
0.97830
0.67608
I-OI334
0.72586
1.05092
0.77745
i-55
0.98449 0.53405
1.01700
0.57678
1.05205
0.62095
1.08973
0.66667
1.13013
0.71406
1.6
1.04742 0.48335
1.08201
0.52202
1.11930
0.56199
I.I5939
0.60337
1.20238
0.64626
1.65
1. 10390 0.42966
1. 14035
0.46403
1. 17965
0-49957
1. 22194
0.5363S
1.26722
0.57448
i-7
1. 15356 0.37332
1.19166
0.40319
1.23274
0.43407
I.27689
0.46603
1.32425
0.49916
i-7S
1.19613 0.31469
1.23563
0.33986
1.27822
0.36589
I.32400
0.39283
1.37309
0.42076
1.8
1. 23132 0.25411
1. 27198
0.27444
1.31582
0.29546
1.36294
0.31721
1.41348
0.33976
1.85
1.25891 0.19197
1.30048
0.20732
I.34530
0.22320
1-39349
0.23964
1. 445 1 6
0.25667
1.9
1.27874 0.12864
1.32097
0.13893
1.36650
0.14957
I-4I544
0.16058
1.46793
0.17200
1-95
1.29069 0.06452
I-3333I
0.06968
1.37927
0.07502
I.42867
0.08054
1. 48 1 64
0.08627
2.0
1.29468 0.00
1-33743
0.00
1.38353
0.00
1.43309
0.00
1.48623
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (0.9 + i 1.0) = o + i 1.02652.
cosh (0.9 + i 1. 10) = 0.22418 + i 1.01388.
[61]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
x = 1.05
X = LIS
1.54308
0.00
1.60379
0.00
1.66852
0.00
1-7374*
0.00
1.81066
0.00
0.05
1-53832
0.09221
1.59885
0.09838
1.66337
0.10479
1.73206
0.11147
1.80507
0.1 1 843
O.I
1.52408
0.18384
1-58405
0.19615
1.64798
0.20894
1. 71602
0.22226
1.78836
0.23613
0.15
1.50045
o.27435
1-55948
0.29271
1.62242
0.31 180
1. 68941
0.33167
1.76063
0.35238
0.2
1.46756
0.36316
I-52530
0.38746
1.58685
0.41274
1.65238
0.43904
1.72204
0.46645
0.25
1.42562
0.44973
1.48171
0.47983
I-54I5I
0.51113
1-60517
0-5437I
1.67283
0.57765
0.3
1.37490
0-53353
1.42899
0.56924
1.48666
0.60637
1.54805
0.64502
1-61331
0.68528
0.3s
1-31569
0.61404
1.36746
0.65514
1.42265
0.69787
1-48139
0.74235
I-54384
0.78869
0.4
1.24838
0.69077
1.29750
0.73700
1.34986
0.78508
1.40560
.83511
1.46485
0.88724
0.4s
I-I7337
0.76323
I-2I953
0.81432
1.26875
0.86743
1.32114
0.92272
1.37684
0.98032
-5
1.09112
0.83099
1-13405
0.88661
1. 17982
0.94445
1.22854
1.00464
1.28033
1.06735
o-55
1. 002 1 5
0.89363
1.04158
0-95344
1.08362
1.01564
1. 12836
1.08037
I-I7593
1.14781
0.6
0.90700
0.95076
0.94269
1.01439
0.98073
1.08056
1.02123
1. 14943
1.06428
1.22118
0.65
0.80626
1.00202
0.83798
1 .06909
0.87180
1. 13883
0.90780
1.21141
0.94607
1.28703
0.7
0.70055
1. 047 1 1
0.72811
1.11719
o.75749
1. 19007
0.78877
1.26592
0.82202
1-34494
o.75
0.59051
1.08574
0.61375
1-15841
0.63852
1.23398
0.66488
1-31263
0.69291
1-39456
0.8
0.47684
1.11768
0.49560
1. 19249
0.51560
1.27028
0.53689
1-35124
o.55952
1-43558
0.85
0.36023
1. 14273
o.3744o
1.21921
0.38951
1.29875
0.40559
1-38152
0.42269
1.46776
0.9
0.24139
1. 16073
0.25089
1.23842
0.26101
1. 31920
0.27179
1.40329
0.28325
1.49088
o-95
0.12107
1.17158
0.12583
1.24999
0.1 309 1
I-33I53
0.13632
1.41640
0.14206
1. 50481
1.0
0.00
1. 17520
0.00
1.25386
0.00
I-33565
0.00
1.42078
0.00
1.50946
1. 05
0.12107
1.17158
0.12583
1.24999
0.13091
i-33 J 53
0.13632
1. 4 1 640
0.14206
1. 5048 1
1.1
0.24139
1. 1 6073
0.25089
1.23842
0.26101
1.31920
0.27179
1.40329
0.28325
1.49088
i-i5
0.36023
1. 14273
0.37440
1.21921
0.38951
1.29875
0.40559
1.38152
0.42269
1.46776
1.2
0.47684
1.11768
0.49560
1. 19 249
0.51560
1.27028
0.53689
1-35124
0.55952
1-43558
1.25
0.59051
1.08574
0.61375
1. 1 5841
0.63852
1.23398
0.66488
1.31263
0.69291
1-39456
i-3
0.70055
1. 0471 1
0.7281 1
1.11719
0.75749
1. 19007
0.78877
1.26592
0.82202
1-34494
i-35
0.80626
1.00202
0.83798
1 .06909
0.87180
1. 13883
0.90780
1.22x41
0.94607
1.28703
1.4
0.90700
0.95076
0.94269
1.01439
0.98073
1.08056
1.02123
1 .14943
1.06428
1.22118
1-45
1. 002 1 5
0.89363
1.04158
0-95344
1.08362
1.01564
1. 12836
1 .0803 7
1 17593
1.14781
i-5
1.09112
0.83099
1. 1 3405
0.88661
1. 1 7982
0-94445
1.22854
1 .00464
1.28033
1.06735
i-55
1. 17337
0.76323
1.21953
0.81432
1.26875
0.86743
1.32114
0.92272
1.37684
0.98032
1.6
1.24838
0.69077
1.29750
0.73700
1.34986
0.78508
1.40560
0.83511
1.46485
0.88724
1.65
1. 3 1 569
0.61404
1.36746
0.65514
1.42265
0.69787
1.48139
0.74235
1-54384
0.78869
i-7
1.37490
o.53353
1.42899
0.56924
1.48666
0.60637
1.54805
0.64502
1.61331
0.68528
i-75
1.42562
0.44973
1.48171
0.47983
I-54I5I
0.51113
1. 60517
o.5437i
1.67283
o.57765
1.8
1.46756
0.36316
1-52530
0.38746
1.58685
0.41274
1.65238
0.43904
1.72204
0.46645
1.8s
1.50045
0.27435
1.55948
0.29271
1.62242
0.3 1 180
1. 68941
0.33167
1.76063
0.35238
1.9
1.52408
0.18384
1.58405
0.19615
1.64798
0.20894
1. 71602
0.22226
1.78836
0.23613
1-95
1.53832
0.09221
1.59885
0.09838
1-66337
0.10479
1.73206
0.11147
1.80507
0.1 1 843
2.0
1.54308
0.00
1.60379
0.00
1.66852
0.00
1 -73741
0.00
1 .81066
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (1.2 + to) 1.8 1066 + i o.
cosh (1.1 + i 1.1) = 0.26101 + i 1.31920.
[62]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
x = 1.25
x = 1.3
* = 1.35
x = 1.4
x = 1.45
1.88842
O.00
1.97091
0.00
2.05833
0.00
2.15090
0.00
2.24884
0.00
0.05
1.88260
0.12569
1.96484
I.I3325
2.05200
0.14116
2.14427
0.14941
2.24191
0.15804
O.I
1.86517
0.25060
1.94665
0.26569
2.03299
0.28144
2.12442
0.29790
2.22115
0.31510
0.15
1.83624
0.37396
1. 91646
0.39648
2.00146
0.41999
2.09147
0.44455
2.18671
0.47022
0.2
1.79600
0.49502
1-87445
0.52483
1-95759
0-55595
2.04562
0.58846
2.13878
0.62244
0.25
1.74467
0.61303
1.82089
0.64994
1.90165
0.68848
1-98717
0.72875
2.07766
0.77083
-3
1.68260
0.72726
1. 75610
0.77105
1.83399
0.81677
1. 91 646
0.86454
2.00373
0.91446
0.3S
1.61014
0.83700
1.68048
0.88740
I-75502
0.94002
I.83394
0.99500
I.9I745
1-05245
0.4
1.52777
0.94158
I-5945I
0.99829
1.66523
1.05748
1. 74012
1.11932
i.8i935
1. 1 8396
0-4S
1-43597
1.04036
1.49870
1.10301
1-56517
1. 1 6842
I.63556
1.23674
1. 71007
1.30817
-5
1-33532
1. 13273
I.39365
1.20094
I.45546
1. 27215
1.52092
I-34655
1-59017
1.4243 1
o-SS
1.22643
1.21811
1. 28001
1. 29146
1.33678
I.36804
1.39690
1 .44804
1.4605 1
i.53i66
0.6
1. 10999
1.29598
1. 15848
1.37402
1.20986
I-45550
1.26427
1. 5406 1
1.32184
1.62958
0.65
0.98670
I.36586
1.02980
1. 448 1 1
1.07548
I.53398
1. 1 2384
1.62369
1. 17502
I-7I745
0.7
o-85733
1.42732
0.89478
L5I327
0.93446
1.60300
0.97649
1.69675
1.02095
1-79473
o.75
0.72267
1.47998
0.75424
1.56910
0.78769
1. 66215
0.8231 1
1-75934
0.86060
1.86094
0.8
0.58355
I.52352
0.60905
1.61526
0.63606
1.71104
0.66466
1.81110
0.69493
1.91569
0.85
0.44084
I.55766
0.46010
1.65146
0.48051
I.74938
0.50212
1.85169
0.52498
1.95862
0.9
0.29541
1.58220
0.30832
1.67747
0.32199
1.77694
0.33647
1.88086
0.35180
1.98947
o-95
0.14816
1.59698
0.15464
I.693I5
0.16150
1-79354
0.16876
1.89843
0.17644
2.00806
1.0
0.00
1.60192
0.00
1.69838
0.00
1.79909
0.00
1.90430
0.00
2.01427
1.05
0.14816
1.59698
0.15464
i-(>92,i-S
0.16150
1-79354
0.16876
1.89843
0.17644
2.00806
1.1
0.29541
1.58220
0.30832
1.67747
0.32199
1.77694
0.33647
1.88086
0.35180
1.98947
I.I5
0.44084
1-55766
0.46010
1.65146
0.48051
1.74938
0.50212
1.85169
0.52498
1.95862
1.2
0.583S5
I.52352
0.60905
1.61526
0.63606
1.71104
0.66466
1.81110
0.69493
1.91569
1.35
0.72267
1.47998
0.75424
1.56910
0.78769
1.66215
0.82311
1-75934
0.86060
1.86094
i-3
0.85733
1.42732
0.89478
1-51327
0.93446
1.60300
0.97649
1.69675
1.02095
1-79473
1-35
0.98670
1.36586
1.02980
1. 448 1 1
1.07548
I.53398
1. 12384
1.62369
1. 17502
I-7I745
1.4
1. 1 0999
1.29598
1. 1 5848
1.37402
1.20986
I-45550
1.26427
1. 54061
1.32184
1.62958
1. 45
1.22643
1.21811
1. 28001
1. 29146
1.33678
1.36804
1.39690
1 .44804
1. 4605 1
1.53166
i-5
1.33532
1. 13273
I.39365
1.20094
I.45546
1. 27215
1.52092
I-34655
1.59017
1. 4243 1
i-55
1-43597
1.04036
1.49870
1.10301
1-56517
1. 16842
163556
1.23674
1.71007
1-30817
1.6
1.52777
0.94158
I-5945I
0.99829
1.66523
1.05748
1. 74012
1-11932
1.81935
1. 1 8396
1.6s
1.61014
0.83700
I.68048
0.88740
1.75502
0.94002
1.83394
0.99500
I-9I745
1.05245
i-7
1.68260
0.72726
I.75610
0.77105
1.83399
0.81677
1. 9 1 646
0.86454
2.00373
0.91446
I.75
1.74467
0.61303
I.82089
0.64994
1.90165'
0.68848
1.98717
0.72875
2.07766
0.77083
1.8
1.79600
0.49502
1.87445
0.52483
1-95759
o.55595
2.04562
0.58846
2.13878
0.62244
1.85
1.83624
0.37396
1. 9 1 646
0.39648
2.00146
0.41999
2.09147
0.44455
2.18671
0.47022
1.9
1.86517
0.25060
1.94665
0.26569
2.03299
0.28144
2.12442
0.29790
2.22115
0.31510
1-95
1.88260
0.12569
1 .96484
0.13325
2.05200
0.14116
2.14427
0.14941
2.24191
0.15804
2.0
1.88842
0.00
1. 9709 1
0.00
2.05833
0.00
2.15090
0.00
2.24884
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (1.4 + i i-o) = 2.12442 + i 0.29790.
cosh (1.4 + i 1^) = 1.26427 + i 1. 54061.
[63]
Table VIII. HYPERBOLIC COSINES, cosh (* 4- iq) = u + iv. Continued
x = 1.5
x = 1.55
x = 1.6
x = 1.65
x = 1.7
2.3S241
0.00
2.46186
0.00
2.57746
0.00
2.69952
0.00
2.82832
0.00
0.05
2.34516
0.16706
2.45427
0.17650
2.56952
0.18639
2.69121
0.19673
2.81960
0.20757
O.I
2.32345
0.33309
2.43I55
0.35192
2-54573
0.37162
2.66629
0.39225
2-79350
0.41387
0.15
2.28742
0.49707
2.39384
0.52516
2.50625
0.55456
2.62494
0.58536
2.75017
0.61761
0.2
2.23727
0.65798
2.34137
0.69517
2.45I3 1
0.73409
2.56740
0.77485
2.68989
0.81754
0.25
2.17334
0.81484
2.27446
0.86089
2.38127
0.90909
2.49404
o.95957
2.61302
1. 01 244
-3
2.09601
0.96667
2.19353
1.02130
2.29654
1.07848
2.40529
1-13837
2.52005
1. 20109
o-3S
2.00576
1.11255
2.09908
1. 17542
2.19765
1. 24123
2.30173
1.31015
2.41154
1.38234
0.4
1. 903 14
1. 25156
1. 99 1 69
1.32229
2.08522
1.39632
2.18396
147385
2.28816
i.555o6
o-45
1.78879
1.38286
1. 87201
1.46101
1.95992
1.54281
2.05274
1.62847
2.15067
1. 71820
-5
1-66341
1-50563
1.74080
1-59071
1.82254
1.67978
1.90885
I.77305
1.99992
1.87074
o.55
1.52777
1.61912
1.59885
1. 71062
1-67393
1.80640
1.75320
1.90669
1.83684
2.01175
0.6
1.38271
1.72263
1.44704
1.81997
1.51500
1.92187
1.58674
2.02858
1.66244
2.14036
0.65
1. 22913
1.81551
1.28632
1.91811
1.34672
2.02550
1.41050
2.13797
1.47779
2.25577
0.7
1.06797
1.89720
1.11766
2.00442
1.17015
2.11664
1.22556
2.23417
1.28403
2-35727
0-7S
0.90023
1.96720
0.9421 1
2.07837
0.98636
2.19473
1.03306
2.31660
1.08235
2.44424
0.8
0.72693
2.02507
0.76076
2.I395I
0.79648
2.25930
0.83420
2.38474
0.87400
2.51614
0.85
0.54916
2.07045
o.5747i
2.18745
0.60170
2.30993
0.63019
2.43818
0.66026
2.57253
0.9
0.36800
2.10307
0.38512
2.22191
0.40320
2.34632
0.42230
2.47659
0.44245
2.61306
o-95
0.18457
2.12272
0.19316
2.24268
0.20223
2.36824
0.21 180
2-49973
0.22191
2.63747
1.0
0.00
2.12928
0.00
2.24961
0.00
2-37557
0.00
2.50747
0.00
2.64563
1.05
0.18457
2.12272
0.19316
2.24268
0.20223
2.36824
0.21180
2-49973
0.22191
2.63747
1.1
0.36800
2.10307
0.38512
2.22191
0.40320
2.34632
0.42230
2.47659
0.44245
2.61306
i-i5
0.54916
2.07045
o.5747i
2.18745
0.60170
2.30993
0.63019
2.43818
0.66026
2.57253
1.2
0.72693
2.02507
0.76076
2-13951
0.79648
2.25930
0.83420
2.38474
0.87400
2.51614
1.25
0.90023
1.96720
0.9421 1
2.07837
0.98636
2.19473
1.03306
2.31660
1.08235
2.44424
i-3
1.06797
1.89720
1.11766
2.00442
1.17015
2.11664
1.22556
2.23417
1.28403
2.35727
i-3S
1. 22913
1.81551
1.28632
1.91811
1.34672
2.02550
1.41050
2.13797
1.47779
2-25577
1.4
1.38271
1.72263
1.44704
1.81997
1.51500
1.92187
1.58674
2.02858
1.66244
2.14036
i-45
1.52777
1.61912
1.59885
1. 71062
1-67393
1 .80640
1-75320
1.90669
1.83684
2.01175
i-5
1.66341
1-50563
1.74080
1-59071
I.82254
1.67978
1.90885
I-77305
1.99992
1.87074
i-55
1.78879
1.38286
1.87201
1.46101
1.95992
1.54281
2.05274
1.62847
2.15067
1. 71820
1.6
1.903 14
1. 25156
1. 99 1 69
1.32229
2.08522
1.39632
2.18396
I-47385
2.28816
i.555o6
1.65
2.00576
1.11255
2.09908
1. 17542
2.19765
1. 24123
2.30173
1.31015
2.41 1 54
1.38234
i-7
2.09601
0.96667
2.19353
1.02130
2.29654
1.07848
2.40529
1-13837
2.52005
1. 20109
1-75
2.17334
0.81484
2.27446
0.86089
2.38127
0.90909
2.49404
o.95957
2.61302
1.01244
1.8
2.23727
0.65798
2.34137
0.69517
2.45131
0.73409
2.56740
0.77485
2.68989
0.81754
1.8S
2.28742
0.49707
2.39384
0.52516
2.50625
o.55456
2.62494
0.58536
2.75017
0.61761
1.9
2.32345
0.33309
2.43155
0.35192
2-54573
0.37162
2.66629
0.39225
2.79350
0.41387
i-95
2.34516
0.16706
2.45427
0.17650
2.56952
0.18639
2.69121
0.19673
2.81960
0.20757
2.0
2.35241
0.00
2.46186
0.00
2.57746
0.00
2.69952
0.00
2.82832
0.00
Note. Negative quantities are in heavy type.
Examples, cosh (1.6 + i 0.4) = 2.08522 4- i 1.39632.
cosh (1.7 + i 1.2) = 0.87400 4- i 2.51614.
[64]
Table VIII. HYPERBOLIC COSINES, cosh (* + iq) - u + iv. Continued
x = 1.75
x = 1.8
x = 1.85
x = 1.9
x - I-9S
2.96419
0.00
3.10747
0.00
3-25853
0.00
3-41773
0.00
3.58S48
0.00
0.0s
2-9550S
0.21893
3.09789
0.23084
3.24848
0.24332
3.40719
0.25642
3-57443
0.27015
O.I
2.92769
0.43652
3.06921
0.46026
3.21841
0.48627
3.37565
0.51125
3-54134
0.53864
0.15
2.88229
0.65141
3.02161
0.68684
3.16850
0.72398
3.32330
0.76294
3.48641
0.80380
0.2
2.81911
0.86229
2.95538
0.90918
3.09904
0.95835
3.25045
1.00992
3.41000
1. 0640 1
0.25
2.73855
1.06784
2.87093
1. 12592
3.01049
1.18681
3-15757
1.25067
3-31255
1. 31766
-3
2.64111
1.26682
2.76878
J-33572
2.90337
1.40796
3.04522
I.48372
3.19469
1. 563 18
o.35
2.52739
1-45799
2.64956
1-53728
2.77835
1.62042
2.91409
1. 90761
3-o57i3
1.79907
0.4
2.39808
1. 64016
2.51400
1.72937
2.63620
1.82289
2.76501
I.92098
2.90071
2.02387
-45
2-25399
1. 81223
2.36294
1.91079
2.47780
2.01413
2.59887
2.12250
2.72642
2.23618
0.5
2.09600
1-973*2
2.19731
2.08043
2.30413
2.19294
2.41670
2.31094
2-53532
2.43471
o.55
1.92509
2.12185
2.01814
2.23725
2.11624
2.35824
2.21964
2.48513
2.32858
2.61823
0.6
1. 74231
2.25749
1.82653
2.38027
I.9I53I
2.50900
2.00889
2.64400
2.10749
2.78561
0.65
1.54878
2.37922
1.62365
2.50862
1.70258
2.64429
I.78576
2.78657
1-87341
2.93582
0.7
I-3457I
2.48627
1.41076
2.62149
1-47934
2.76327
1-55162
2.91 196
1.62777
3.06792
0-7S
I-I3435
2.57800
1.18918
2.71821
1.24698
2.86522
1.30791
3-OI939
1.37210
3.18111
0.8
0.91599
2-65384
0.96026
2.79817
1.00694
2.94950
1.05614
3.10821
1. 10797
3.27468
0.85
0.69198
2.71331
0.72542
2.86088
0.76069
3.01560
0.79785
3.I7787
0.83701
3-34807
0.9
0.46370
2.75606
0.48612
2-90595
0.50975
3.063 1 1
0.53465
3-22793
0.56089
3.40081
-95
0.23257
2.78181
0.24381
2.93310
0.25566
3-09173
0.26815
3.25809
0.28131
3-43259
1.0
0.00
2.79041
0.00
2.94217
0.00
3.10129
0.00
3.26816
0.00
3-44321
1.05
0.23257
2.78181
0.24381
2.93310
0.25566
2.09173
0.26815
3.25809
0.28131
343259
1.1
0.46370
2.75606
0.48612
2.90595
0.50975
3.063 1 1
0.53465
3.22793
0.56089
3.40081
i-i5
0.69198
2.71331
0.72542
2.86088
0.76069
3.01560
0.79785
3.17787
0.83701
3.34807
1.2
0.91599
2.65384
0.96026
2.79817
1.00694
2.94950
1.05614
3.10821
1. 1 0797
3.27468
1-25
I.I3435
2.57800
1.18918
2.71821
1.24698
2.86522
1.30791
3-OI939
1.37210
3.18111
i-3
I-3457I
2.48627
1.41076
2.62149
1.47934
2.76327
1.55162
2.91196
1.62777
3.06792
i-3S
I.54878
2.37922
1.62365
2.50862
1.70258
2.64429
1.78576
2.78657
1.87341
2.93582
1.4
1. 7423 1
2.25749
1.82653
2.38027
i-9i53i
2.50900
2.00889
2.64400
2.10749
2.78561
i-45
1.92509
2.12185
2.01814
2.23725
2.11624
2.35824
2.21964
2.48513
2.32858
2.61823
i-5
2.09600
1.97312
2.19731
2.08043
2.30413
2.19294
2.41670
2.31094
2.53532
2-43471
i-S5
2.25399
1.81223
2.36294
1. 91079
2.47780
2.01413
2.59887
2.12250
2.72642
2.23618
1.6
2.39808
1. 64016
2.51400
1.72937
2.63620
1.82289
2.76501
1.92098
2.90071
2.02387
1. 65
2.52739
1-45799
2.64956
I.53728
2.77835
1.62042
2.91409
1.90761
3-05713
1.79907
i-7
2.641 1 1
1.26682
2.76878
1-33572
2.90337
1.40796
3.04522
1-48372
319469
1.56318
i-75
2.73855
1.06784
2.87093
1. 12592
3.01049
1.18681
3.15757
1.25067
3.31255
1. 3 1 766
1.8
2.81911
0.86229
2.95538
0.90918
3.09904
0.95835
3.25045
1.00992
3.41000
1. 06401
1.85
2.88229
0.65141
3.02161
0.68684
3-16850
0.72398
332330
0.76294
3.48641
0.80380
1.9
2.92769
0.43652
3.06921
0.46026
3.21841
0.48627
3.37565
0.51125
3.54134
0.53864
i-9S
2.95505
0.21893
3.09789
0.23084
3.24848
0.24332
3.40719
0.25642
3-57443
0.27015
2.0
2.96419
0.00
3-10747
0.00
3.25853
0.00
3-41773
0.00
3.58548
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (1.8 +
io.2) = 2.
95538 + 1
I 0.90918.
[65]
Table VIII. HYPERBOLIC COSINES, cosh (* + iq) = u + iv. Contlnued
x = 2.05
x = 2.15
3.76220
0.00
3-94832
0.00
4.14431
0.00
4-35o67
0.00
4.56791
0.00
0.05
3-7SOS9
0.28456
3-936i5
0.29968
4-I3I54
o.3i555
4-33726
0.33221
4-55382
0.34970
O.I
3-7I587
0.56737
3.89971
o.5975i
4.09329
0.62916
4.29711
0.66237
4.51167
0.69724
0.15
3-65825
0.84667
3-83923
0.89166
4.02981
0.93888
4.23046
0.98845
4.44170
1 .04049
0.2
3-578o6
1. 12076
3-75507
1. 18032
3.94148
1.24282
4-13773
1.30844
4-34433
1-37732
0.25
3-4758i
1.38794
3-64777
1. 46 1 69
3.82885
i-539i
4.01950
1.62035
4.22019
1.70566
0.3
3-35214
1.64656
3-5I798
I.73405
3.69261
1.82589
3.87647
1.92228
4.07003
2.02349
o-35
3.20780
1.89503
3-36649
1-99573
3-5336i
2.10142
'3.70956
2.21236
3.89478
2.32883
0.4
3.04368
2.13182
3.19426
2.24509
3-35283
2.36399
3-5I977
2.48879
3-69552
2.61982
o.45
2.86080
2.35546
3.00232
2.48062
3-I5I37
2.61 199
3-30828
2.74988
3-47347
2.89466
0.5
2.66027
2.56458
2.79188
2.70085
2.93048
2.84389
3-07639
2.99402
3.23000
3-15165
0-5S
2-44335
2.75789
2.56423
2.90443
2.69152
3-05825
2-82553
3.21970
2.96661
3.38921
0.6
2.21136
2.93420
2.32076
3.0901 1
2-43597
3-25376
2.55726
3-42553
2.68495
3.60588
0.65
1.96574
3.09241
2.06299
3-23673
2.16540
3.42920
2.27322
3.61024
2.38672
3.80031
0.7
1.70800
3.23156
1.79250
3-40327
1.88148
3-5835I
1.97516
3.77269
2.07379
3-97I3I
o.75
1-43973
3-35078
1.51096
3-52883
1.58596
3-7I57I
1.66493
3.91188
1.74806
4-11783
0.8
1. 16258
3-44935
1. 22010
3.63264
1.28066
3.82501
1-34443
4.02695
1.41156
4.23896
0.85
0.87827
3.52666
0.92172
3.71404
0.96747
3.91074
1.01564
4.11720
1.06636
4-33396
0.9
0.58854
3.58221
0.61765
3-77256
0.64831
3-97235
0.68059
4.18206
0.71458
4.40223
o-95
0.29518
3.61568
0.30978
3.80781
0.32516
4.00946
.34i35
4-22113
o-35839
4-44337
1.0
0.00
3.62686
0.00
3-81958
0.00
4.02186
0.00
4.23419
0.00
4-457"
1. 05
0.29518
3-61568
0.30978
3.80781
0.32516
4.00946
o.34i35
4-22113
0.35839
4-44337
1.1
0.58854
3.58221
0.61765
3-77256
0.64831
3-97235
0.68059
4.18206
0.71458
4.40223
MS
0.87827
3.52666
0.92172
3.71404
0.96747
3.91074
1. 01564
4.11720
1.06636
4-33396
1.2
1. 16258
3-44935
1. 22010
3.63264
1.28066
3.82501
1.34443
4.02695
1.41156
4.23896
1.25
1-43973
3-35078
1. 51096
3-52883
1.58596
3-7I57I
1.66493
3.9H88
1.74806
4-11783
i-3
1.70800
3- 2 3 I 56
1.79250
3-40327
1.88148
3-5835I
i.975i6
3.77269
2.07379
3-97i3i
1-35
1.96574
3.09241
2.06299
3-23673
2.16540
3.42920
2.27322
3.61024
2.38672
3.80031
1.4
2.21136
2.93420
2.32076
3.0901 1
2-43597
3-25376
2.55726
3-42553
2.68495
3.60588
i-45
2-44335
2.75789
2.56423
2.90443
2.69152
3-05825
2.82553
3.21970
2.96661
3.38921
i-5
2.66027
2.56458
2.79188
2.70085
2.93048
2.84389
307639
2.99402
3.23000
3-15165
i-55
2.86080
2-35546
3.00232
2.48062
3.I5I37
2.61199
3-30828
2.74988
3-47347
2.89466
1.6
3.04368
2.13182
3.19426
2.24509
3.35283
2.36390
3-51977
2.48879
3-69552
2.61982
1.65
3.20780
1.89503
336649
1-99573
353361
2.10142
370956
2.21236
3.89478
2.32883
1.7
3.35214
1.64656
3.51798
I-73405
3.69261
1.82589
3.87647
1.92228
4.07003
2.02349
i-75
3-4758I
1.38794
3.64777
1. 46 1 69
3.82885
1-5391
4.01950
1.62035
4.22019
1.70566
1.8
3.578o6
1. 12076
3.75507
1. 18032
3.94148
1.24282
4-13773
1.30844
4-34433
1-37732
1.8S
3.65825
0.84667
383923
0.89166
4.02981
0.93888
4.23046
0.98845
4.44170
1.04049
1.9
3.7I587
0.56737
3.89971
o.5975i
4.09329
0.62916
4.2971 1
0.66237
4.51167
0.69724
i-95 v
3.75059
0.28456
393615
0.29968
4.I3I54
-3i555
4-33726
0.33221
4-55382
o.3497o
2.0
3.76220
0.00
3.94832
0.00
4-I443I
0.00
4-35067
0.00
4.56791
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (2.1 4- i 0.8) = 1.28066 4- i 3.82501.
cosh (2.2 + i 1.25) = 1.74806 + J4.11783.
[66]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
x = 2.25
x = 2.3
* = 2.35
x = 2.4
x = 2.45
4-79057
0.00
5.03722
0.00
5.29047
0.00
5-55695
0.00
5-83732
0.00
0.05
4.78178
0.36807
5.02169
0.38735
5.27416
0.40760
5-5398i
0.42888
5-8i933
0.45122
O.I
4-73751
0.73386
4-97521
0.77231
5-22533
0.81269
5-48853
0.85511
5-76545
0.89966
0.15
4.66404
1 .95 13
4.89805
1-15251
5.14429
1. 21277
5-4034I
1.27607
5.67603
1-34255
0.2
4.56181
1.44965
4.79058
1.52560
5-03153
1.60537
5.28496
1.68916
5-55i62
1. 77716
0.25
4-43145
I.79523
4-65378
1.88930
4.88776
1.98808
5-13394
2.09184
5-39298
2.20082
0.3
4-27377
2.12975
4.48820
2.24134
4.71384
2-35853
4-95 I2 7
2.48162
5.20109
2.61091
o-3S
4.08975
2.45"3
4.29494
2-57956
4.51087
2-71443
4.73808
2.85610
4-977I3
3.00490
0.4
3.88050
2.75740
4.07520
2.90188
4.28008
3-05360
449567
3.21297
4.72249
3-38036
0-4S
3-64734
3.04677
3-83034
3.20630
4.02290
3-37395
4-22554
3-55003
4-43873
3-73499
0.5
3.39168
3.31716
3-56185
3.49096
3-74093
3-6735I
3-92935
3.86521
4.12761
4.06659
o-55
3-11512
3-567I9
3-27141
3-754IO
3-43588
3-95038
3.60894
4.15656
3.79104
4-373"
0.6
2.81935
3-79523
2.96081
3.99409
3.10966
4.20292
3.26629
4.42228
3-43109
4.65268
0.65
2.50620
3-99987
2.63194
4.20946
2.76426
4-42955
2.90349
4.66073
3.04999
4-90356
0.7
2.17760
4.17986
2.28685
4.39887
2.40182
4.62887
2.52280
4.87045
2.65009
5.12420
o.75
1-83557
4-33407
1.92766
4.56116
2.02457
4-79965
2.12655
5.05014
2.23385
5-3I325
0.8
1.48222
4.46157
I.55659
4-69533
1.63485
4.94083
1.71719
5.19869
1.80383
5-46955
0.85
1.11974
4-56I55
1. 17592
4.80056
1.23504
5-05156
1.29724
5-3I52I
1.36269
5-592I3
0.9
0.75035
4-6334I
0.78799
4.87618"
0.82761
5-i3 ir 4
0.86930
5-39893
0.91316
5.68022
0-9S
0.37633
4.67671
0.39522
4.92174
0.41509
5.17909
0-43599
5-44938
o.45799
5-73330
1.0
0.00
4.691 1 7
0.00
4.93696
0.00
5-i95io
0.00
5.46623
0.00
5-75103
1. o S
0.37633
4.67671
0.39522
4.92174
0.41509
5.17909
0-43599
5-44938
0-45799
5-73330
1.1
0.75035
4-6334I
0.78799
4.87618
0.82761
5-I3II4
0.86930
5-39893
0.91316
5.68022
i-i5
1.11974
4-56I55
1. 17592
4.80056
1.23504
5-05156
1.29724
5-3I52I
1.36269
5.592I3
1.2
1.48222
4.46157
I.55659
4-69533
1.63485
4.94083
1.71719
5.19869
1.80383
5-46955
1-25
1.83557
4-33407
1.92766
4.56116
2.02457
4-79965
2.12655
5.05014
2.23385
5-3J325
i-3
2.17760
4.17986
2.28685
4.39887
2.40182
4.62887
2.52280
4.87045
2.65009
5.12420
i-3S
2.50620
3-99987
2.63194
4. 20946
2.76426
4-42955
2.90349
4.66073
3.04999
4-90356
1.4
2.81935
3-79523
2.96081
3.99409
3.10966
4.20292
3.26629
4.42228
343109
4.65268
1-45
3.11512
3-567I9
3.27141
3-7541
3.43588
3-95038
3.60894
4.15656
3.79104
4-373 11
i-5
3-39168
3.31716
3-56185
3.49096
3.74093
3-6735I
392935
3.86521
4.12761
4.06659
i-55
3.64734
3.04677
3-83034
3.20630
4.02290
3-37395
4-22554
3-55003
4-43873
3-73499
1.6
3-88050
2.75740
4.07520
2.90188
4.28008
3-05360
4.49567
3.21297
4.72249
3-38036
1.65
4.08975
2-45H3
4.29494
2-57956
4.51087
2.71443
4.73808
2.85610
4-97713
3.00490
i-7
4-27377
2.12975
4.48820
2.24134
4.71384
2-35853
4.95127
2.48162
5.20109
2.61091
i-7S
4-43145
1-79523
4-65378
1.88930
4.88776
1.98808
5-13394
2.09184
539298
2.20082
1.8
4.56181
1.44965
4.79058
1.52560
503153
1-60537
5.28496
1. 689 1 6
v55i62
1. 77716
1.85
4.66404
1-09513
4.89805
1-15251
5.14429
1. 21277
5-4034I
1.27607
5-67603
1-34255
1.9
4-73751
0.73386
4-97521
0.77231
5-22533
0.81269
5-48853
0.85511
5.76545
0.89966
i-9S
4.78178
0.36807
5.02169
0.38735
5.27416
0.40760
5.53981
0.42888
5.8I933
0.45122
2.0
4.79657
0.00
5.03722
0.00
5.29047
0.00
5.55695
0.00
583732
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (2.4 4- J04) = 4-495 6 7 + * 3-21297-
cosh (2.4 + i 1^5) == -3-92935 + ' 3-86521
[67]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) m % + iv. Continued
x = 2.5
* = 2.55
X = 2.6
x = 2.65
x = 2.7
6.13229
0.00
6.44259
0.00
6.76901
0.00
7-11234
0.00
7-47347
0.00
0.0s
6.11339
0.47469
6.42273
0-49935
6.74814
0.52526
7.09042
0.55249
7-45043
0.58109
O.I
6.05680
0.94646
6.36327
0.99563
6.68567
1.04729
7.02478
1.10156
7.38146
1-15859
0.15
5.96287
1-41239
6.26458
I-48577
6.58199
1.56285
6.91583
1.64385
7.26697
1.72896
0.2
5-83215
1. 8696 1
6.12727
1.96674
6.43770
2.06878
6.76424
2.17600
7.10769
2.28866
0.25
5-66550
2-3I53I
5-952i8
2-43559
6.25374
2.56196
6.57095
2.69474
6.90458
2.83425
c-3
5-46392
2.74674
5-74039
2.88943
6.03123
3-03934
6.33714
3.19686
6.65891
3-36237
o-3S
5.22864
3.16122
5-49321
3-32545
5-77153
3-49799
6.06427
3.67927
6.37218
3.86976
0.4
4.961 13
3-55622
5.21217
3-74097
5.47624
3-935o6
5-75401
4.13900
6.04606
4-35329
o.45
4.66304
3.92929
4.89898
4-I3342
5-I47I9
4.34788
5-40827
4-57321
5.68287
4.80998
0.5
4-336i9
4.27814
4-5556o
4-50039
4.78641
4-73389
5.02919
4-97923
5-28454
5.23702
o-55
3.98260
4.60062
4-18413
4.83961
4.39612
5.09071
4.61910
5-35454
4-85363
5-63I77
0.6
3.60448
4.89472
3.78686
5.14900
3.97872
5-4i6i5
4.18053
5-69685
4-39279
5-99179
0.65
3.20411
5-I5865
3.36624
5.42664
3-5368o
5.70819
3-71619
6.00403
3.90488
6.31488
0.7
2.78401
5-39077
2.92488
5.67082
3.07306
5-96505
3.22894
6.27419
3-39288
6.59903
0-7S
2-34673
5.58966
2.46547
5.88004
2.59039
6.18512
2.72178
6.50567
2.85997
6.84249
0.8
1.89498
5-75408
1.99087
6.05301
2.09174
6.36706
2.19784
6.69705
2-30943
7-04377
0.85
I-43I5S
5-88304
I-50399
6.18866
1.58019
6.50976
1.66034
6.84713
1.74465
7.20163
0.9
o-9593o
5-97572
1.00784
6.28615
1. 0589 1
6.61231
1.11262
6.95500
1.16911
7-3i5o8
o.95
0.481 13
6.03155
0.50548
6.34489
0.53109
6.67409
0.55803
7.01998
0.58636
7-38343
1.0
0.00
6.05020
0.00
6.36451
0.00
6.69473
0.00
7.04169
0.00
7.40626
1.05
0.481 13
6.03155
0.50548
6.34489
0.53109
6.67409
0.55803
7.01998
0.58636
7-38343
1.1
0.95930
5-97572
1.00784
6.28615
1.05891
6.61231
1.11262
6.95500
1.16011
7-3i5o8
US
1. 43 1 55
5.88304
1.50399
6.18866
1.58019
6.50976
1.66034
6.84713
1.74465
7.20163
1.2
1.89498
5-754o8
1.99087
6.05301
2.09174
6.36706
2.19784
6.69705
2.30943
7-04377
1-25
2.34673
5.58966
2.46547
5.88004
2.59039
6.18512
2.72178
6.50567
2.85997
6.84249
i-3
2.78401
5-39077
2.92488
5.67082
3.07306
5-96505
3.22894
6.27419
3-39288
6-59903
1-35
3.2041 1
5-15865
3.36624
5.42664
353680
5.70819
3-71619
6.00403
3.90488
6.31488
1.4
3.60448
4.89472
3.78686
5.14900
3.97872
5-4i6i5
418053
5.69685
4.39279
5-99179
1 -45
3.98260
4.60062
4.18413
4.83961
4.39612
5.09071
4.61910
5-35454
485363
5-63I77
i-5
4-336I9
4.27814
4.55560
4-50039
4.78641
4-73389
5-02919
4-97923
5-28454
5.23702
i-55
4.66304
3.92929
4.89898
4.13342
5.I47I9
4.34788
5.40827
4-57321
5.68287
4.80998
1.6
4.961 13
3-55622
5.21217
3-74097
5.47624
3-935o6
5-75401
4.13900
6.04606
4-35329
1.65
5.22864
3.16122
5-49321
3-32545
5-77153
3-49799
6.06427
3.67927
6.37218
3-86976
i-7
5-46392
2.74674
5.74039
2.88943
6.03123
3-03934
6.33714
3.19686
6.65891
3-36237
i-7S
5-66550
2-3I53I
5.95218
2-43559
6.25374
2.56196
6.57095
2.69474
6.90458
2.8342 s
1.8
5-832I5
1. 86961
6.12727
1.96674
6.43770
2.06878
6.76424
2.17600
7.10769
2.28866
1.8s
5.96287
1.41239
6.26458
I-48577
6.58199
1.56285
6.91583
1.64385
7.26697
1.72896
1.9
6.05680
0.94646
6.36327
o-99563
6.68567
1.04729
7.02478
1.10156
7.38146
1-15859
i-95
6.H339
0.47469
6.42273
0-49935
6.74814
0.52526
7.09042
0.55249
7-45043
0.58109
2.0
6.13229
0.00
6.44259
0.00
6.76901
0.00
7.1 1234
0.00
7-47347
0.00
Note. Negative quantities are in heavy type.
Examples, cosh (2.7 + i 1.00) = o + * 7.40626.
cosh (2.6 + i 1^2) = 2.09174 + i 6.36706.
[68]
Table VIII. HYPERBOLIC COSINES, cosh (* + iq) = u + iv. Continued
x = 2.75
x = 2.80
x = 2.85
x = 2.90
x = 2.95
7-85328
0.00
8.25273
0.00
8.67281
0.00
9.11458
0.00
9-579*5
0.00
0.05
7.82907
0.61115
8.22728
0.64273
8.64608
0.67592
9.08649
0.71081
9.54962
0.74747
O.I
7-75659
1. 21852
8.15112
1. 28150
8.56604
1.34768
9.00237
1-41723
9.461 21
1.49032
0.15
7.63629
1.81839
8.02470
1.91237
8.43318
2.01112
8.86275
2.11491
9-31447
2.22399
0.2
7.46891
2.40704
7.84881
2.53I44
8.24834
2.66217
8.66850
2.79956
9. 1 103 1
2-94395
0.25
7-2S548
2.98086
7.62452
3.I349I
8.01263
3.29681
8.42078
3.46694
8.84998
3-64575
-3
6.99732
3-53629
7-35323
3-7I905
7-72754
3.91112
8.12115
4. 1 1 295
8.53508
4.32508
o-35
6.69602
4.06993
7.03661
4.28026
7-39479
4-50131
7.77146
4-7336i
8.16757
4-97774
0.4
6-35344
4-57847
6.67660
4.81509
7.01646
5-06375
7-37385
5-325o8
7.74969
5.63048
o-45
5.97168
5-05878
6.27542
5.32022
6.59486
5.59498
6.93078
5-88371
7.28404
6.18717
o-5
5-553"
5-50790
5-83556
5-79256
6.13261
6.09170
6.44498
6.40608
6.77348
6.73647
o-55
5.10030
5-92307
5-35972
6.22918
5-63254
6.55088
5-9I945
6.88894
6.22116
7.24424
0.6
4.61604
6.30172
4.85083
6.62740
5-09775
6.96966
5-35742
7-32934
5.63048
7.70735
0.65
4-10333
6.64151
4.31204
6.98476
4-53153
7-34547
4.76236
7-72455
5.00509
8.12294
0.7
3-5653I
6.94036
3.74666
7.29905
3-93738
7-67599
4-13793
8.07213
4.34884
8.48845
o.75
3-oo532
7.19642
3-i58i8
7-56834
3-31894
7-959I9
3.48800
8.36994
3.66578
8.80162
0.8
2.42680
7.4081 1
2.55023
7.79098
2.68005
8.19332
2.81656
8.61616
2.96012
9-06053
0.85
1-83331
7-57413
1.92656
7-96557
2.02463
8.37694
2.12776
8.80924
2.23621
9.26358
0.9
1.22852
7-69345
1.29101
8.09106
I-35673
8.50891
1-42583
8.94802
1-49851
9.40952
o-95
0.61616
7-76534
0.64750
8.16666
0.68046
8.58841
0.71512
9.03163
0-75*57
9.49744
1.0
0.00
7-78935
0.00
8.19192
0.00
8.61497
0.00
9-05956
0.00
9.52681
1. 05
0.61616
7-76534
0.64750
8.16666
0.68046
8.58841
0.71512
9.03163
o.75i57
9.49744
1.1
1.22852
7-69345
1.29101
8.09106
135673
8.50891
1.42583
8.94802
1.49851
9.40952
i-i5
1-83331
7-574I3
1.92656
7-96557
2.02463
8.37694
2.12776
8.80924
2.23621
9.26358
1.2
2.42680
7.4081 1
2.55023
7.79098
2.68005
8.19332
2.81656
8.61616
2.96012
9.06053
1.25
3.00532
7.19642
3-15818
7-56834
331894
7-959*9
3.48800
8.36994
3.66578
8.80162
i-3
3.56531
6.94036
3.74666
7.29905
393738
7-67599
4-13793
8.07213
4.34884
8.48845
1-35
410333
6.64151
4.31204
6.08476
4-53153
7-34547
4.76236
7-72455
5.00509
8.12294
1.4
4.61604
6.30172
4-85083
6.62740
5-09775
6.96966
5-35742
7.32934
5.63048
7-70735
1-45
5.10030
5-92307
5-35972
6.22918
5-63254
6.55088
5.91945
6.88894
6.22116
7.24424
i-S
5-553 1 1
5-50790
583556
5-79256
6.13261
6.09170
6.44498
6.40608
6.77348
6.73647
i-55
5.97168
5-05878
6.27542
5.32022
6.59486
5-59498
6.93078
5-88371
7.28404
6.18717
1.6
6-35344
4-57847
6.67660
4.81509
7.01646
5-06375
7.37385
5-32508
7.74969
5.63048
1. 65
6.69602
4.06993
7.03661
4.28026
7-39479
4-50131
7.77146
4.73361
8.16757
4-97774
i-7
6.99732
3-53629
7-35323
3-7I90S
7.72754
3.91112
8.12115
4-11295
8.53508
4.32508
i-75
7.25548
2.98086
7.62452
3-I349I
8.01263
3.29681
8.42078
3.46694
8.84998
'3-64575
1.8
7.46891
2.40704
7.84881
2.53144
8.24834
2.66217
8.66850
2.79956
9.11031
2-94395
1.8s
7.63629
1.81839
8.02470
1.91237
8.43318
2.01112
8.86275
2.11491
9-31447
2.22399
1.9
7.75659
1. 21852
8.15112
1. 28150
8.56604
1.34768
9.00237
1-41723
9.46121
1.49032
1-95
7.82907
0.61115
8.22728
0.64273
8.64608
0.67592
9.08649
0.71081
9.54962
o.74747
2.0
7.85328
0.00
8.25273
0.00
8.67281
0.00
9.11458
0.00
9-57915
0.00
Note.
Negative quantities are in heavy type.
Examples, cosh (2.95 + i o) = 9.57915 + i o.
cosh (2.8 + i 1^ = 2.55023 + i 7.79098.
[69]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
x = 3.0
* = 3-5
X m 3.10
x = 3-*5
* = 3.20
10.06766
0.00
10.58135
0.00
11.12150
O.00
11.68946
0.00
12.28665
0.00
0.05
10.03660
0.78599
10.54870
0.82649
11.08720
0.86905
11.65340
0.91378
12.24880
0.96080
O.I
9-94371
1.56714
10.451 10
1.64788
10.98460
I.73274
U-54550
1-82193
12.13540
1.91568
0.1s
9.78949
2.33863
10.28900
2.4591 1
10.81420
2.58575
11.36650
2.71885
11.94720
2.85874
0.2
9-57492
3-09569
10.06350
3-255I8
10.57720
3.42281
11.11730
3-59900
11.68530
3.78419
0.25
9.30131
3-83368
9-77589
4.03120
10.27490
4.23878
10.79970
4.45696
11.35140
4.68630
o-3
8.9703S
4.54806
9.42805
4-78233
9-90933
5.02860
10.41540
5-28745
10.94750
5-55952
o-3S
8.58409
5-23433
9.02209
5.50400
9.48264
5-78743
9.96690
6.08533
10.47610
6.39846
0.4
8.14491
5-88836
8.56049
6.19173
8-99749
6.51058
945697
6.84570
9.9401 1
7-19795
0.4s
7-6SS5I
6.50609
8.04612
6.84128
8.45686
7-I9358
8.88873
7-56387
9.34284
7-953o6
0.5
7.11891
7.08371
7.48215
7.44866
7.86409
7.83223
8.26570
8.23539
8.68797
8.65915
o-5S
6.53842
7.61765
6.87204
8.01011
7.22284
8.42260
7.59170
8.85615
7-97954
9-31184
0.6
5.91762
8.10463
6.21956
8.52218
6.53705
8.96104
6.87089
9.42230
7.22191
9.90712
0.65
5.26034
8.54164
5-52874
8.98171
5.81097
9-44423
6.10773
9-93036
6.41976
10.44130
0.7
4.57062
8.92599
4.80383
9-38586
5.04906
9.86919
5.30690
10.37720
5-578o2
10.91120
o.75
3-85273
9-25531
4.04931
9.73216
4.25602
10.23330
4.47336
10.76010
4.70190
"3I370
0.8
3.11108
9-52757
3.26982
10.01840
3-43673
10.53430
3.61224
11.07660
3.79678
11.64650
0.85
2.35025
9.74108
2.47017
10.24290
2.59626
10.77040
2.72885
11.32480
2.86826
11.90750
0.9
1-57493
9.89454
1.65529
10.40430
1-73979
10.94010
1.82863
11.50320
1.92205
12.09510
o-95
0.78990
9.98699
0.83020
10.50150
0.87258
11.04230
0.91714
11. 61070
0.96400
12.20810
1.0
0.00
10.01787
0.00
io.53399
0.00
11.07645
0.00
1 1. 64661
0.00
12.24588
1. 05
0.78990
9.98699
0.83020
10.50150
0.87258
11.04230
0.91714
11. 61070
0.96400
12.20810
1.1
1-57493
9.89454
1.65529
10.40430
1-73979
10.94010
1.82863
11.50320
1.92205
12.09510
i-i5
2.35025
9.74108
2.47017
10.24290
2.59626
10.77040
2.72885
11.32480
2.86826
11.90750
1.2
3.11108
9-52757
3.26982
10.01840
3-43673
10.53430
3.61224
11.07660
379678
11.64650
1-25
3-85273
9-25531
4.04931
9.73216
4.25602
10.23330
4-47336
10.76010
4.70190
11.31370
i-3
4.57062
8.92599
4.80383
9.38586
5.04906
9.86919
5.30690
10.37720
5-57802
10.91120
i-35
5.26034
8.54164
5-52874
8.98171
5.81097
9.44423
6.10773
9-93036
6.41976
10.44130
1.4
5-91762
8.10463
6.21956
8.52218
6.53705
8.96104
6.87089
9.42230
7.22191
9.90712
i-45
6.53842
7.61765
6.87204
8.01011
7.22284
8.42260
7.59170
8.85615
7-97954
9.3 1 1 84
i-5
7.11891
7.08371
7.48215
7.44866
7.86409
7.83223
8.26570
8-23539
8.68797
8.65915
i-S5
7-65551
6.50609
8.04612
6.84128
8.45686
7-I9358
8.88873
7-56387
9.34284
7-953o6
1.6
8.14491
5-88836
8.56049
6.19173
8.99749
6.51058
9-45697
6.84570
9.9401 1
719795
1.65
8.58409
5-23433
9.02209
5.50400
9.48264
5.78743
9.96690
6.08533
10.47610
6.39846
i-7
8.97035
4.54806
9.42805
4-78233
9-90933
5.02860
10.41540
5-28745
10.94750
5-55952
i-75
9-30I3I
3-83368
9-77589
4.03120
10.27490
4-23878
10.79970
4.45696
11.35140
4.68630
1.8
9-57492
3-09569
10.06350
3-255I8
10.57720
3.42281
11.11730
3-59900
11.68530
3.78419
1.85
9.78949
2.33863
10.28900
2.4591 1
10.81420
2.58575
11.36650
2.71885
11.94720
2.85874
1.9
9-94371
1. 56714
10.45110
1.64788
10.98460
I.73274
H-54550
1. 82193
12.13540
1. 9 1 568
i-9S
10.03660
0.78599
10.54870
0.82649
11.08720
0.86905
11.65340
0.91378
12.24880
0.96080
2.0
10.06766
0.00
10.58135
0.00
11.12150
0.00
11.68946
0.00
12.28665
0.00
Note. Negative quantities are in heavy type.
Examples, cosh (3.10 + i 0.5) = 7.86409 -f- i 7.83223.
cosh (3.10 + i 1.55) = -8.45686 + i 7.19358.
[70]
Table VIII. HYPERBOLIC COSINES.
cosh (x
-f- iq) = u
+ iv . Continued
?
x =
3-25
X =
3-30
x =
3-35
x =
3-4o
* =
3-45
o
12.91456
0.00
13-57476
0.00
14.26891
0.00
14.99874
0.00
15.76607
0.00
0.05
12.87474
1.01022
13-53290
1.06217
14.22498
1.11677
14.95250
1-17417
15.71746
1.23450
O.I
12.75555
2.01422
13.40764
2.11780
14.09323
2.22666
14.81410
2.341 10
I5-57I96
2.46139
0.15
12.55773
3-oo579
13.19970
3.16036
13-87465
3.32282
14.58432
3-49359
I5-33045
3.67311
0.2
12.28247
3-97883
12.91035
4-18343
I3-57054
4-39850
14.26465
4.62455
14.99442
4.86217
0.25
11.93150
4-92735
12.54145
5.18072
13.18275
5.44705
13.85702
5.72700
I4-56595
6.02127
0.3
11.50695
S-84548
12.09520
6.14670
12.71369
6.46202
I3-363Q7
6.79414
14.04764
7.14324
o-35
11.01147
6.72758
11.57440
7-07352
12.16623
7.437I5
12.78852
7.81938
13.44278
8.22116
0.4
10.44810
7.56820
10.98222
7-95737
n-54379
8.36643
12.13423
8.79642
12.75501
9.24840
o.4S
9.82031
8.36217
10.32233
8.79215
10.85016
9.24413
11.40512
9.71923
1 1. 9886 1
10.21863
0.5
9.13197
9.10456
9-59881
9-57273
10.08964
10.06483
10.60570
10.58212
1 1. 14830
11. 12585
o.55
8.38733
9.79082
8.81610
10.29428
9.26691
10.82349
9.74090
n-37975
10.23924
11.96447
0.6
7-59099
10.41673
7-97905
10.95235
8.38705
ii-5i54i
8.81604
12.10723
9.26706
12.72933
0.65
6.74784
10.97841
7.09279
11.54294
7-45549
12.13633
7.83682
12.76006
8.23775
I3-4I572
0.7
5.86309
11.47240
6.16381
12.06234
6-47795
12.68244
6.80928
I3-33423
7-I5765
14.01940
0-7S
4.94218
11.89566
5-19485
12.50736
5-46075
13-15033
5-73977
13.82620
6.03341
14.53662
0.8
3.99082
12.24560
4.19483
12.87530
4-40933
I3.537I7
4.63487
14.23291
4.87198
14.96423
0.85
3.01484
12.52002
3.16897
13.16388
3-33ioi
13.84054
3-5 OI 39
I4-55I88
3-68053
15.29960
0.9
2.02028
12.71726
2.21356
13.37120
2.23215
14.05851
2.34632
14.78111
2.46636
15.54061
0-9S
1.01326
12.83610
1.06507
I3-496I5
I-H953
14.18950
1. 17679
14.91923
1.23699
15.68581
1.0
0.00
12.87578
0.00
13-53788
0.00
14.23382
0.00
14.96536
0.00
I5-73432
1.05
1. 01326
12.83610
1.06507
i3-49 6l 5
I-H953
14.18950
1. 17679
14.91923
1.23699
15.68581
1.1
2.02028
12.71726
2.12356
13.37120
2.23215
14.05851
2.34632
14.78111
2.46636
15.54061
i-iS
3.01484
12.52002
3.16897
13.16388
3-33IOI
13.84054
3-5oi39
14.55188
3-68053
15.29960
1.2
3.99082
12.24560
4.19483
12.87530
4.40933
i3-537!7
4.63487
14.23291
4.87198
14.96423
1-25
4.94218
11.89566
5-19485
12.50736
5-46075
13-15033
5-73977
13.82620
6.03341
14.53662
i-3
5-86309
11.47240
6.16381
12.06234
6-47795
12.68244
6.80928
I3-33423
7-I5765
14.01940
1-35
6.74784
10.97841
7.09279
11.54294
7-45549
12.13633
7.83682
12.76006
8.23775
I3-4I572
1.4
7-59099
10.41673
7-97905
10.95235
8.38705
ii-5i54i
8.81604
12.10723
9.26706
12.72933
1 -45
8.38733
9.79082
8.81610
10.29428
9.26691
10.82349
9.74090
u-37975
10.23924
11.96447
1-5
9-i3i97
9.10456
9*-5988i
9-57273
10.08964
10.06483
10.60570
10.58212
11. 14830
11. 12585
1-55
9.82031
8.36217
10.32233
8.79215
10.85016
9.24413
1 1.405 1 2
9.71923
1 1. 9886 1
10.21863
1.6
10.44810
7.56820
10.98222
7-95737
H-54379
8.36643
12.13423
8.79642
12.75501
9.24840
1.6S
11.01147
6.72758
11.57440
7-07352
12.16623
7-43715
12.78852
7.81938
13.44278
8.22116
1-7
11.50695
5-84548
12.09520
6.14670
12.71369
6.46202
13.36397
6.79414
14.04764
7.14324
1-75
11.93150
4-92 735
12.54145
5.18072
13-18275
5-44705
13.85702
5.72700
14.56595
6.02127
1.8
12.28247
3-97883
12.91035
4-18343
I3.57054
4-39850
14.26465
4-62455
14.99442
4.86217
1.85
12.55773
3-oo579
13.19970
3.16036
13.87465
3.32282
14.58432
3-49359
15-33045
3.67311
1.9
12.75555
2.01422
13.40764
2. 1 1 780
14.09323
2.22666
14.81410
2.341 10
15-57196
2.46139
1-95
12.87474
1.01022
13-53290
1. 062 1 7
14.22498
1.11677
14.95250
1.17417
15.71746
i-2345o
2.0
12.91456
0.00
13-57476
0.00
14.26891
0.00
14.99874
0.00
15.76607
0.00
Note. Negative quantities are in heavy type.
Examples, cosh (3.45 + i 0.05) 15.71746 + * 1.23450.
cosh (3.25 + i 1.95) = 12.87474 + i 1.01022.
[7i]
Table VIII. HYPERBOLIC COSINES, cosh (x + iq) = u + iv. Continued
q x = 3.50
o 16.57282 0.00
0.05 16.52173 1.29792
0.1 16.36878 2.58783
0.15 16.11491 3.86180
0.2 15.76170 5.11195
0.25
-3
o.35
0.4
o.45
0.5
0-5S
0.6
0.65
0.7
0-7S
0.8
0.85
0.9
o-95
1.0
1.05
1.1
iiS
1.2
1.25
i-3
i-35
1.4
1 -45
i-5
i-5S
1.6
1.6S
i-7
i-75
1.8
1.85
1.9
i-95
15.31130 6.33059
14.76650 7.51020
14.13065 8.64360
13.40770 9.72361
12.60210 10.74357
11.69740
12.57910
13-3833
14.10490
14.73960
15.28340
i5-733oo
16.08555
16.33896
16.49163
11. 71820
10.76320
9.74126
8.65928
7.5 2 39i
6.34215
5.12129
3-86885
2.59256
1.30029
0.00 16.54263
1.30029 16.49163
2.59256 16.33896
3.86885 16.08555
5.12129 15.73300
6.34215 15-28340
7.52391 14.73960
8.65928 14.10490
9.74126 13.38330
10.76320 12.57910
11. 71820 11.69740
12.60210 10.74357
13.40770 9.72361
14.13065 8.64360
14.76650 7.51020
15-31130 6.33059
15.76170 5-HI9S
16.11491 3.86180
16.36878 2.58783
16.52173 1.29792
2.0 16.57282 0.00
* = 3-55
17.42102 0.00
17.36731 1.36458
17.20653 2.72075
16.93970 4.06015
16.56840 5.37451
16.09492 6.65574
15.52225 7.89594
14.85386 9.08745
14.09390 10.22293
13.24705 11.29540
12.31852 12.29820
11.31405 13.22520
10.23982 14.07066
9.10246 14.82933
7.90898 15-49665
6.66674 16.06840
5.38339 16.54105
4.06686 16.91 1 75
2.72525 17.17817
1.36684 17-33870
0.00 17.39230
1.36684 17-33870
2.72525 17.17817
4.06686 16.91 1 75
5-38339 16.54105
6.66674 16.06840
7.90898 15.49665
9.10246 14.82933
10.23982 14.07066
11. 31405 13.22520
12.31852 12.29820
13-24705 11.29540
14.09390 10.22293
14.85386 9.08745
15-52225 7-89594
16.09492 6.65574
16.56840 5.37451
16.93970 4.06015
17.20653 2.72075
17.36731 1.36458
17.42102 0.00
x = 3.60
18.31278 0.00
18.25632 1.43466
18.08732 2.86047
17.80680 4.26865
17.41650 5-65052
16.91880 6.99754
16.31680 8.30143
15.61421 9-55412
14.81535 10.74789
13.92515 11.87545
12.94910 12.92978
11.89320 13.90436
10.76400 14.79326
9.56840 15.59090
8.31383 16.29246
7.00800 16.89356
5.65896 17.39050
4.27503 17.78022
2.86475 18.06033
1.43680 18.22900
0.00 18.28546
1.43680 18.22900
2.86475 18.06033
4.27503 17.78022
5.65896 17-39050
7.00800 16.89356
8.31383 16.29246
9.56840 15.59090
10.76400 14.79326
11.89320 13.90436
12.94910 12.92978
13-92515 11-87545
14-81535 10.74789
15.61421 9.55412
16.31680 8.30143
16.91880 6.99754
17.41650 5.65052
17.80680 4.26865
18.08732 2.86047
18.25632 1.43466
18.31278 0.00
x = 3-65
19.25033 0.00
19.19100 1.50832
19.01331 3.00735
18.71843 4.48783
18.30814 5.94065
17.78497 7.35683
17.152.r6 8.72766
16.41360 10.04469
15.57383 11.^9972
14.63806 12.48520
13.61203 13.59365
12.50208 14.61830
"31505 15.55281
10.05827 16.39143
8.73946 17.12900
7.36678 17.76096
5.94868 18.28342
4.49390 18.69316
3.01 142 18.98765
1.51036 19.16506
0.00 19.22434
I. 51036 19.16506
3.01 142 18.98765
4.49390 18.69316
5.94868 18.28342
7.36678 17.76096
8.73946 17.12900
10.05827 16.39143
11.31505 15.55281
12.50208 14.61830
13.61203 1*3.59365
14.63806 12.48520
15.57383 11.29972
16.41360 10.04469
17.15216 8.72766
17.78497 7.35683
18.30814 5.94065
18.71843 4-48783
19.01331 3.00735
19.19100 1.50832
19.25033 0.00
x = 3.70
20.23601 0.00
20.17362 1.58576
19.98688 3.16174
19.67690 4.71823
19.24560 6.24563
18.69565 7-73453
18.03040 9-17573
17.25404 10.56037
16.37127 11.87990
15.38760 13.12620
14.30902 14.29155
13.14223 15.36878
11.89444 16.35127
10.57330 17-23295
9.18696 18.00840
7.74399 18.67280
6.25327 19.22208
4.72401 19.65290
3.16561 19.96246
1.58770 20.14900
0.00 20.21129
1.58770 20.14900
3.16561 19.96246
4.72401 19.65290
6.25327 19.22208
7-74399 18.67280
9.18696 18.00840
10.57330 17.23295
11.89444 16.35127
13.14223 15.36878
14.30902 14.29155
15.38760 13.12620
16.37127 11.87990
17.25404 10.56037
18.03040 9.17573
18.69565 7-73453
19.24560 6.24563
19.67690 4.71823
19.98688 3. 16 1 74
20.17362 1.58576
20.23601 0.00
Note. Negative quantities are in heavy type.
Examples, cosh (3.50 -+- i 0.70) = 7.52391 + i 14.73960.
cosh (3.60 + i 1.55) = -13.92515 + i 11.87545.
[72]
Table VIII. HYPERBOLIC COSINES, cosh (* + iq) = u + iv. Continued
* = 3-75
x = 3.80
o 21.27230
0.05 21.20670
0.1 21.01038
0.15 20.68452
0.2 20.23113
0.25
o-3
0-35
0.4
0-4S
o.75
0.8
0.85
0.9
0.9S
1.0
1.05
I.I
J
1.2
1.25
i-3
1-35
1.4
1. 45
I -5
x -55
1.6
1.65
*-7
i-75
1.8
1.85
1.9
i-9S
0.00
1.66716
3-32404
4.96043
6.56624
19.65301 8.13156
18.95373 9- 6 4674
18.13760 11. 10246
17.20963 12.48971
16.17556 I3-79998
0.5 15.04177 15.02516
o.55 13-81524 16.15770
0.6 12.50353 17.19062
0.65 11.11473 18.11756
0.7 9.65741 18.93280
8.14055 19.6313 1
6-57350 20.20879
4.96592 20.66167
3.32772 20.98716
1.66900 21.18327
0.00 21.24878
1.66900 21.18327
3.32772 20.98716
4.96592 20.66167
6.57350 20.20879
8.14055 19.63131
9.65741 18.93280
11.11473 18.11756
12.50353 17.19062
13.81524 16.15770
15.04177 15.02516
16.17556 13.79998
17.20963 12.48971
18.13760 11. 10246
18.95373 9-64674
19.65301 8.13156
20.23113 6.56624
20.68452 4.96043
21.01038 3.32404
21.20670 1.66716
22.36178
22.29283
22.08646
21.74391
21.26731
0.00
1-75273
3-49465
5-21503
6.90325
2.0 21.27230 0.00
20.65958 8.54892
19.92448 10.14188
19.06655 11.67230
18.09105 13.13076
17.00402 14.50828
15.81 216 15.79634
14.52281 16.98701
13.14392 18.07296
11.68400 19.04746
10.15203 19.90455
8.55748 20.63891
6.91017 21.24603
5.22025 21.72216
3.49815 22.06437
1.75448 22.27052
0.00 22.33941
1.75448 22.27052
3.49815 22.06437
5.22025 21.72216
6.91017 21.24603
8.55748 20.63891
10.15203 19.90455
11.68400 19.04746
13-14392 18.07296
14.52281 16.98701
15.81216 15.79634
17.00402 14.50828
18.09105 13.13076
19.06655 11.67230
19.92448 10.14188
20.65958 8.54892
21.26731 6.90325
21.74391 5-21503
22.08646 3.49465
22.29283 1.75273
22.36178 0.00
* = 3-85
23.50717 0.00
23.43470 1.84268
23-21775 3-67400
22.85766 5.48267
22.35664 7-25754
21.71778 8.98766
20.94503 10.66233
20.04315 12.27134
19.01770 13.80465
17.87500 15.25286
16.62208 16.60702
15.26668 17.85880
13.81716 19.00048
12.28246 20.02501
10.67203 20.92608
x = 3.90
24.71135 0.00
24.63516 1.93724
24.40710 3.86254
24.02856 5.76402
23.50188 7.62997
22.83030 9.44887
22.01797 11.20952
21.06988 12.90106
19.99190 14-51307
18.79065 16.03558
17-47355 I7-45924
16.04874 18.77526
14.52497 19.97556
12.91164 21.05272
11.21871 21.99993
8.99580
21.69813
9.45662
22.81160
7.26411
22.33640
7.63623
23.48262
5.48764
22.83696
5-76875
24.00888
3.67733
23.19673
3-86571
24.38710
1-84435
23.41348
1.93883
24.61500
0.00
23.48589
0.00
24.69110
1.84435
23.41348
1.93883
24.61500
3.67733
23.19673
3.86571
24.38710
5.48764
22.83696
5.76875
24.00888
7.2641 1
22.33640
7.63623
23.48262
8.99580 21.69813
10.67203 20.92608
12.28246 20.02501
13.81716 19.00048
15.26668 17.85880
16.62208 16.60702
17.87500 15.25286
19.01770 13.80465
20.04315 12.27134
20.94503 10.66233
21.71778 8.98766
22.35664 7-25754
22.85766 5.48267
23.21775 3-67400
23.43470 1.84268
23.50717 0.00
9.45662 22.81160
11.21871 21.99993
12.91164 21.05272
14.52497 19.97556
16.04874 18.77526
17.47355 17-45924
18.79065 16.03558
19.99190 14-51307
21.06988 12.90106
22.01797 11.20952
22.83030 9.44887
23.50188 7-62997
24.02856 5.76402
24.40710 3.86254
24.63516 1.93724
24.71135 0.00
x - 3-95
25.97731 0.00
25.89724 2.03665
25.65749 4.06074
25-25957 6.05979
24.70590 8.02149
23.99991 9.93373
23.14597 11.78474
22.14931 13.56305
21.01610 15.25776
19.75331 16.85842
18.36873 18.35512
16.87098 19.73867
15.26910 21.00052
I3-573I5 22.13290
11.79366 23.12881
9.94109 23.98212
8.02744 24.68760
6.06429 25.24084
4.06375 25.63849
2.03816 25.87805
0.00 25.95806
2.03816 25.87805
4.06375 25.63849
6.06429 25.24084
8.02744 24.68760
9.94109 23.98212
11.79366 23.12881
I3.573I5 22.13290
15.26910 21.00052
16.87098 19.73867
18.36873 18.35512
19-75331 16.85842
21.01610 15.25776
22.14931 13.56305
23-14597 11-78474
23.99991 9-93373
24.70590 8.02149
25-25957 6.05979
25-65749 4-06074
25.89724 2.03665
25.97731 0.00
Note. Negative quantities are in heavy type.
Examples, cosh (3.90 + i 0.25) = 22.83030 + i 9.44887.
cosh (3.75 + i 1.25) = -8.14055 4- i 19.63131.
[73]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) = u + iv
o
0.05
O.I
0.15
0.2
0.25
o-3
o-3S
0.4
o.45
-5
o.55
0.6
0.65
0.7
o.75
0.8
0.85
0.9
-95
1.0
1.05
1.1
i-i5
1.2
1-25
1.3
i-35
1.4
i-4S
i-5
i-SS
1.6
1.6s
i-7
1-75
1.8
1.8s
1.9
1 -95
x = o
0.00 0.00
0.00 0.07870
0.00 0.15838
0.00 0.24008
0.00 0.32492
0.00 0.41421
0.00 0.50953
0.00 0.61280
0.00 0.72654
0.00 0.85408
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1. 0000
1.1 7085
1.37638
1.63185
1. 96 261
2.41421
3.07768
4.16530
6.3137S
12.70620
12.70620
6.3137S
416530
3.07768
2.41421
1.96261
1. 63 1 85
1.37638
1. 1 7085
0.00 1. 0000
0.00 0.85408
0.00 0.72654
0.00 0.61280
0.00 0.50953
0.00 0.41421
0.00 0.32492
0.00 0.24008
0.00 0.15838
0.00 0.07870
0.00 0.00
x = 0.05
0.04996 0.00
0.05027 0.07850
0.05121 0.15798
0.05283 0.23944
0.05522 0.32402
0.05850 0.41300
0.06289 0.50792
0.06865 0.61070
0.07623 0.72378
0.08624 0.85040
0.09967
0.1 1804
0.14392
0.18179
0.24007
0.33624
0.51 109
0.87867
1.85674
5.79801
20.01667
5.79801
1.85674
0.87867
0.5 1 109
0.33624
0.24007
0.18179
0.14392
0.1 1804
0.99503
1.16395
1.36649
1.61702
1.93900
2.37365
2.999 1 1
3.98246
5.72808
9.05499
0.00
9.05499
5.72808
3.98246
2.9991 1
2.37365
1.93900
1. 61702
1.36649
1. 16395
0.09967 0.99503
0.08624 0.85040
0.07623 0.72378
0.06865 0.61070
0.06289 0.50792
0.05850 0.41300
0.05522 0.32402
0.05283 0.23944
O.05I 21 O.15798
O.O5027 O.O785O
O.O4996 O.OO
O.O9967 O.OO
O.IOO28 O.07792
O.I02I4 O.I5677
0.10535 O.23755
0.1 1008 0.32136
0.1 1657 0.40940
0.12522 0.50317
0.13659 0.60446
0.15149 0.71557
0.17113 0.83951
0.19738 0.98033
0.23313 1. 14365
0.28315 1.33754
0.35567 1.57401
0.46575 1.87150
0.64333 2.25941
0.95397 2.78504
1.56000 3.51765
2.91746 4.47780
6.21808 4-83133
10.03331
6.21808
2.91746
1.56000
o-95397
0.64333
0.4657S
0.35567
0.28315
0.23313
0.19738
0.17113
0.15149
0.13659
0.12522
0.11657
0.1 1008
0.10535
0.10214
0.10028
0.00
483133
4.47780
351765
2.78504
2.25941
1.87150
1.57401
1-33754
1. 14365
0.98033
0.83951
0.71557
0.60446
0.50317
0.40940
0.32136
0.23755
0.15677
0.07792
0.09967 0.00
x = 0.15
0.14889 0.00
0.14979 0.07695
0.15254 0.15479
0.15727 0.23446
0.16422 0.31698
0.17377 0.40350
0.18647 0.49538
0.20310 0.59427
0.22484 0.70222
0-25339 0.82186
0.29131 0.95663
0.34258 1.11113
0.41357 1. 29164
0.51496 1.50674
0.66202 1.75880
0.90034 2.09061
1.28858 2.48723
1.97316 2.94167
3.22989 3.27758
5.28217 2.71349
6.71659 0.00
5.28217 2.71349
3.22989 3-27758
1.97316 2.94167
1.28858 2.48723
0.90034 2.09061
0.66202 1.75880
0.51496 1.50674
0.41357 1.29164
0.34258 1.11113
0.29131 0.95663
0.25339 0.82186
0.22484 0.70222
0.20310 0.59427
0.18647 0.49538
0.17377 0.40350
0.16422 0.31698
0.15727 0.23446
0.15254 0.15479
0.14979 0.07695
0.14889 0.00
0.19738 0.00
0.19855 0.07562
0.20213 0.15207
0.20828 0.23021
0.21732 0.31098
0.22970 0.39543
0.24613 0.48477
0.26758 0.58044
0.29549 0.68417
0.33192 0.79813
Q-37995
0.92501
0.44423
1.06819
0.53203
1-23185
0.65502
1.42088
0.83268
1.64005
1.09837
1.89083
1.50982
2.16055
2.16111
2.38860
3-I5925
2.37676
4-39854
1.67517
5.06649
0.00
4.39854
1-67517
3-I5925
2.37676
2.16111
2.38860
1.50982
2.16055
1.09837
1.89083
0.83268
1.64005
0.65502
1.42088
0.53203
1.23185
0.44423
1. 068 19
o-37995
0.92501
0.33192
0.79813
0.29549
0.68417
0.26758
0.58044
0.24613
0.48477
0.22970 0.39543
0.21732 0.31098
0.20828 0.23021
0.20213 0.15207
0.19855 0.07562
0.19738 0.00
Note. Negative quantities are in heavy type.
Examples, tanh (o + * 0.95) o + 12.70620.
tanh (o + i 1.45) = o i 1. 17085.
[74]
Table IX. HYPERBOLIC TANGENTS, tanh (* + iq) =u+ iv. Continued
x = 0.25
-3
x = 0.35
x = 0.4
x = 0.45
0.24492
0.00
0.29131
0.00
0.33638
0.00
0-37995
0.00
0.42190
0.00
0.05
0.24635
0.07395
0.29296
0.07199
0.3*322
0.34384
0.06975
0.38196
0.06728
0.42405
0.06462
O.I
0.25069
0.14866
0.29799
0.14464
0.14007
0.38808
0.13503
0.43056
0.1 2961
0.15
0.25814
0.22490
0.30660
0.21864
0.35346
0.21153
0-39853
0.20373
0.44169
o.i9534
0.2
0.26907
0.30351
0.31921
0.29471
0.36750
0.28475
0.41376
0.27384
0.45784
0.26216
0.25
0.28402
0.38540
0.33640
0.37362
0.38658
0.36035
0.43438
0.34585
0.47964
0.33039
0.3
0.30377
0.47162
0.35903
0.45623
0.41161
0.43898
0.46130
0.42022
0.50796
0.40033
o-3S
0.32947
0-56335
0.38833
o.54348
0.44383
0.52131
0.49575
0-49737
0-54397
0.47216
0.4
0.36272
0.66200
0.42600
0.63638
0.48497
0.60802
o.5394i
0.57764
0.58924
0-54593
o-4S
0.40582
0.76919
0.47444
0.73604
0-53739
0.69969
o.5945o
0.66 1 16
0.64580
0.62138
0.5
0.46212
0.88682
0.53705
0.84355
0.60437
0.79671
0.66404
0.74770
0.71630
0.69779
o-55
0.5365S
1. 01699
0.61869
0.95983
0.69041
0.89893
0.75200
0.83632
0.80407
0.7736s
0.6
0.63656
1.16180
0.72640
1-08513
0.80176
1. 005 19
0.86357
0.92478
0.91321
0.84608
0.65
o.77356
1.32269
0.87037
1.21810
0.94684
1.11212
1.00528
1.00856
1 .04844
0.91003
0.7
0.96528
1.49862
1. 065 2 1
i.3536o
1. 13666
1. 21222
1. 1 8469
1.07919
1. 2 1438
0.95708
o-7S
1. 23914
1.68151
1-33091
1.47820
1-38412
1.29020
1.40896
1.12181
I-4I397
0.97400
0.8
1.63553
1.84484
1.69121
1.56140
1.70028
I.3I745
1.68068
1.11235
1.64487
0.94186
0.85
2.20223
1.91863
2.16210
I-54I77
2.08309
1.24667
1.98936
1.01695
1.89366
0.83750
0.9
2.95122
I-750H
2.71602
1.31829
2.49443
1.01613
2.29855
0.79978
2.12957
0.64107
o-95
3.72316
1.11789
3.21905
0.79096
2.83603
0.58484
2.53928
0.44728
2.30471
0.35122
1.0
4.08299
0.00
343274
0.00
2.97287
0.00
2.63193
0.00
2.37024
0.00
1. 05
3.72316
1.11789
3.21905
0.79096
2.83603
0.58484
2.53928
0.44728
2.30471
0.35122
1.1
2.95122
1.75011
2.71602
1. 31829
2-49443
1.01613
2.29855
0.79978
2.12957
0.64107
i-i5
2.20223
1. 9 1 863
2.16210
I-54I77
2.08309
1.24667
1.98936
1.01695
1.89366
0.83750
1.2
1-63553
1.84484
1.69121
1. 56140
1.70028
I-3I745
1.68068
1.11235
1.64487
0.94186
I-2S
1. 23914
1.68151
1.33091
1.47820
1.38412
1.29020
1.40896
1.12181
141397
0.97400
i-3
0.96528
1.49862
1. 065 2 1
1.35360
1. 13666
1. 21222
1. 1 8469
1. 07919
1. 21438
0.95708
i-3S
o.77356
1.32269
0.87037
1.21810
0.94684
1.11212
1.00528
1.00856
1.04844
0.91003
1.4
0.63656
1.16180
0.72640
1.08513
0.80176
1. 00519
0.86357
0.92478
0.91321
0.84608
1 -45
0.53655
1. 01 699
0.61869
0.95983
0.69041
0.89893
0.75200
0.83632
0.80407
0.77365
i-5
0.46212
0.88682
0.53705
0.84355
0.60437
0.79671
0.66404
0.74770
0.71630
0.69779
i-5S
0.40582
0.76919
0.47444
0.73604
0-53739
0.69969
o.5945o
0.66116
0.64580
0.62138
1.6
0.36272
0.66200
0.42600
0.63638
0.48497
0.60802
o.5394i
0.57764
0.58924
0-54593
1.65
0.32947
0.56335
0.38833
0.54348
0.44383
0.52131
0-49575
0-49737
0-54397
0.47216
i-7
0.30377
0.47162
0.35903
0.45623
0.41161
0.43898
0.46130
0.42022
0.50796
0.40033
1,73
0.28402
0.38540
0.33640
0.37362
0.38658
0.36035
0.43438
0.34585
0.47964
0.33039
1.8
0.26907
0.30351
0.31921
0.29471
0.36750
0.28475
0.41376
0.27384
0.45784
0.26216
1.8s
0.25814
0.22490
0.30660
0.21864
o.35346
0.21 153
o.39853
0.20373
0.44169
o.i9534
1.9
0.25069
0.14866
0.29799
0.14464
0.34384
0.14007
0.38808
0.13503
0.43056
0.12961
1 -95
0.24635
0.07395
0.29296
0.07199
0.33822
0.06975
0.38196
0.06728
0.42405
0.06462
2.0
0.24492
0.00
0.29131
0.00
0.33638
0.00
0-37995
0.00
0.42190
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (0.4 4-
* 0.4) = 0.
53941 + 1
1 0.57764.
tanh (0.45 + i 1.75) = 0.47964 - i 0.33039.
[75]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) m u + iv. Continued
x m 0.5
x = 0.55
* = 0.6
x = 0.65
x = 0.7
0.4621 1
0.00
0.50052 0.00
0.53704
0.00
0.57167
0.00
0.60437
0.00
0.05
0.46436
0.06181
0.50284 0.05889
o.5394i
0.05590
0.57405
0.05288
0.60674
0.04984
O.I
0.47119
0.12390
0.50987 0.1 1 796
0.54657
0.1 1 189
0.58125
0.10576
0.61390
0.09962
0.15
0.48281
0.18651
0.52183 0.17737
0.55872
0.16804
0.59344
0.15863
0.62602
0.14925
0.2
0.49964
0.24990
0.53910 0.23725
0.57620
0.22437
0.61094
0.2 1 144
0.64336
0.19858
0.2s
0.52227
0.31424
0.56223 0.29765
C59953
0.28085
0.63419
0. 26404
0.66631
0.24741
03
o.S5i5i
0.37967
0.59196 0.35856
0.62935
o.3373i
0.66377
0.31618
0.69534
0.29540
o-3S
0.58846
0.44616
0.62928 0.41979
0.66653
0-39344
0.70039
0.36748
0.73105
0.34205
0.4
0.63452
0-51350
0.67541 0.48093
0.71212
0.44869
0.74493
0.41714
o.774i3
0.38662
0-4S
0.69149
0.58116
0.73188 0.54121
0.76736
0.50211
0.79836
0.46428
0.82533
0.42806
-5
0.76159
0.64805
0.80050 0.59933
0.83365
0.55229
0.86173
0.50738
0.88535
0.46492
o.55
0.84752
0.71229
0.88332 0.65320
0.91249
0.59707
0.93607
o.54434
0.95480
0.49522
0.6
0.95230
0.77067
0.98247 0.69957
1.00521
0.63346
1.02195
0.57227
1.03389
0.51635
0.65
1.07907
0.81812
1.09973 0.73362
1.11262
0.65676
1.11962
0.58738
1. 12222
0.52508
0.7
1.23020
0.84688
1.23587 0.74858
1.23436
0.66157
1.22793
0.58492
1. 21827
o.5i757
0-75
1.40579
0.84585
1.38926 0.73549
1.36782
0.64076
1.34386
0-5595I
1.31896
0.48976
0.8
1.60095
0.80073
I.55398 0.68387
1.50695
0.58681
1. 46 1 73
0.50588
1.41909
0.43803
0.85
1.80225
0.69623
1. 71785 0.58390
1-64135
0.49366
1. 57271
0.42040
1.51148
0.36034
0.9
1.98505
0.52197
1. 86183 0.43071
1. 75601
0-35949
1.66532
0.30300
1-58713
0.25755
o.95
2.H599
0.28167
1.96180 0.22977
1.83417
0.19009
1.72736
0.15910
1-63711
0.13449
1.0
2.16395
0.00
1.99792 0.00
1.86202
0.00
1.74926
0.00
1.65462
0.00
1. 05
2.11599
0.28167
1.96180 0.22977
1-83417
0.19009
1.72736
0.15910
1.63711
0.13449
1.1
1.98505
0.52197
1.86163 0.43071
1. 75601
o.35949
1.66532
0.30300
1-58713
0.25755
i-i5
1.80225
0.69623
1. 71785 0.58390
1-64135
0.49366
1-57271
0.42040
1. 5 1 148
0.36034
1.2
1.60095
0.80073
1.55398 0.68387
1.50695
0.58681
1-46173
0.50588
1. 41909
0.43803
1.25
1.40579
0.84585
1.38926 0.73549
1.36782
0.64076
1.34386
0-55951
1. 3 1 896
0.48976
i-3
1.23020
0.84688
1.23587 0.74858
1.23436
0.66157
1.22793
0.58492
1. 21827
o.5i757
i-35
1.07907
0.81812
1.09973 0.73362
1.11262
0.65676
1.11962
0.58738
1. 12222
0.52508
1.4
0.95230
0.77067
0.98247 0.69957
1.00521
0.63346
1-02195
0.57227
1.03389
0.51635
i-45
0.84752
0.71229
0.88332 0.65320
0.91249
0.59707
0.93607
0-54434
0.95480
0.49522
i-5
0.76159
0.64805
0.80050 0.59933
0.83365
0.55229
0.86173
0.50738
0.88535
0.46492
i-55
0.69149
0.58116
0.73188 0.54121
0.76736
0.50211
0.79836
0.46428
0.82533
0.42806
1.6
0.63452
0.513SO
0.67541 0.48093
0.71212
0.44869
o.74493
0.41714
o.774i3
0.38662
1.6S
0.58846
0.44616
0.62928 0.41979
0.66653
0-39344
0.70039
0.36748
0.73105
0.34205
i-7
o-55i5i
0.37967
0.59196 0.35856
0.62935
o.3373i
0.66377
0.31618
0.69534
0.29540
i-7S
0.52227
0.31424
0.56223 0.29765
0-59953
0.28085
0.63419
0.26404
0.66631
0.25741
1.8
0.49964
0.24990
0.53910 0.23725
0.57620
0.22437
0.61094
0.21144
0.64336
0.19858
1.85
0.48281
0.18651
0.52183 0.17737
0.55872
0.16804
o.59344
0.15863
0.62602
0.14925
1.9
0.47119
0.12390
0.50987 0.11796
0.54657
0.1 1 189
0.58125
0.10576
0.61390
0.09962
i-95
0.46436
0.06181
0.50284 0.05889
o.5394i
0.05590
0.57405
0.05288
0.60674
0.04984
2.0
0.462 1 1
0.00
0.50052 0.00
0.53704
0.00
0.57167
0.00
0.60437
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (0.6 + ia6) = 1.1
0052 1 +10.63346.
tanh (0.6 + i 1^ = 0.83365 i 0.55229.
[76]
Table IX. HYPERBOLIC TANGENTS, tanh (* + iq) =u+ iv. Continued
x m 0.75
x = 0.85
x = 0.9
x = 0.95
0-63515
0.00
0.66403
0.00
0.69107
0.00
0.71629
0.00
0.73978
0.00
0.05
0.63749
0.04684
0.66633
0.04388
0.69330
0.04099
0.71845
0.03820
0.74185
0.03551
O.I
0.64456
0.09354
0.67325
0.08758
0.70002
0.08176
0.72494
0.07614
0.74807
0.07073
0.15
0.65649
0.13997
0.68490
0.13089
0.71132
0.12206
0.73582
0.1 1354
0.75850
0.10537
0.2
0.67352
0.18592
0.70148
O.I7357
0.72736
0.16160
0.75123
0.15008
0.77321
0.13906
0.25
0.69595
0.23112
0.72325
0.21528
0.74832
0.20001
0.77130
0.18537
0.79231
0.17143
-3
0.72420
0.27516
0.75051
0-25559
0.77446
0.23683
0.79620
0.21893
0.81592
0.20198
-35
0.75872
0.31749
0.78364
0.29392
0.80603
0.27146
0.82611
0.25018
0.8441 1
0.23013
0.4
0.80005
0-35735
0.82300
0.32949
0.84328
0.30314
0.86117
0.27837
0.87695
0.25520
<M5
0.84871
0.39368
0.86893
0.36128
0.88638
0.33091
0.90143
0.30261
0.91438
0.27634
o-5
0.905 15
0.42510
0.92167
0.38798
o.9354i
0-35357
0.94681
0.32181
0.95624
0.29259
o-5S
0.96963
0.44978
0.98122
0.40796
0.99018
0.36966
0.99700
0.33469
1.00211
0.30285
0.6
1.04203
0.46543
1.04722
0.41926
1-05015
o.3775i
1.05136
0.33985
1. 05 1 29
0-30593
0.65
1.12161
0.46934
1.11872
0.42057
1.11427
0.37527
1. 10885
0.33580
1.10271
0.30064
0.7
1.20665
0.45847
I-I9395
0.40661
1.18081
0.36108
1. 16765
0.32108
I-I5485
0.28588
-75
1. 29416
0.42977
1. 27012
0.37806
1.24723
0-3333S
1.22572
0.29458
1.20569
0.26087
0.8
i.3796i
0.38084
I-3433I
0.33238
1.31017
0.29108
1.28006
0.25573
1.25279
0.22532
0.85
I-4570I
0.31065
1.40862
0.26920
1.36562
0.23434
1.32742
0.20483
1.29344
0.17968
0.9
I.5I945
0.22051
1.46062
0.19000
1. 4093 1
0.1 646 1
1.36438
0.14330
i-3 2 493
0.12528
0.9S
1.56023
0.1 1463
1.49428
0.09840
1-43735
0.08499
1.38796
0.07380
1.34490
0.06438
1.0
1-57443
0.00
I-50594
0.00
1.44703
0.00
1.39606
0.00
I-35I75
0.00
1. 05
1.56023
0.11463
1.49428
0.09840
1-43735
0.08499
1.38796
0.07380
1.34490
0.06438
1.1
i-5 I 945
0.22051
1.46062
0.19000
1.4093 1
0.16461
1.36438
0.14330
I-32493
0.12528
i-i5
I-4570I
0.3106s
1.40862
0.26920
1.36562
0.23434
1.32742
0.20483
1.29344
0.17968
1.2
1.37961
0.38084
1 -3433 1
0.33238
1.31017
0.29108
1.28006
0-25573
1.25279
0.22532
1-25
1. 29416
0.42977
1. 27012
0.37806
1.24723
o.33335
1.22572
0.29458
1.20569
0.26087
i-3
1.20665
0.45847
I-I9395
0.40661
1.18081
0.36108
1. 16765
0.32108
1-15485
0.28588
i-3S
1.12161
0.46934
1.11872
0.42057
1.11427
0.37527
1. 10885
0.33580
1.10271
0.30064
1.4
1.04203
0.46543
1.04722
0.41926
1-05015
0.37751
1. 05 1 36
0.33985
1-05129
0.30593
i-45
0.96963
0.44978
0.98122
0.40796
0.99018
0.36966
0.99700
0.33469
1.00211
0.30285
i-5
0.90515
0.42510
0.92167
0.38798
0-9354I
o.35357
0.94681
0.32181
0.95624
0.29259
i-55
0.84871
0.39368
0.86893
0.36128
0.88638
0.33091
0.90143
0.30261
0.91438
0.27634
1.6
0.80005
C35735
0.82300
0.32949
0.84328
0.30314
0.86117
0.27837
0.87695
0.25520
1. 65
0.75872
0.31749
0.78364
0.29392
0.80603
0.27146
.0.82611
0.25018
0.8441 1
0.23013
i-7
0.72420
0.27516
0-75051
0.25559
0.77446
0.23683
0.79620
0.21893
0.81592
0.20198
i-7S
0.69595
0.23112
0.72325
0.21528
0.74832
0.20001
0.77130
0.18537
0.79231
0.17143
1.8
0.67352
0.18592
0.70148
O.I7357
0.72736
0.16160
o-75 I2 3
0.15008
0.77321
0.13906
1.85
0.65649
0.13997
0.68490
0.13089
0.71132
0.12206
0.73582
O.H354
0.75850
0.10537
1,9
0.64456
0.09354
0.67325
0.08758
0.70002
0.08176
0.72494
0.07614
0.74807
0.07073
i-9S
0.63749
0.04684
0.66633
0.04388
0.69330
0.04099
0.71845
0.03820
0.74185
0.03551
2.0
0.63515
0.00
0.66403
0.00
0.69107
0.00
0.71629
0.00
0.73978
0.00
Note. Negative quantities are in heavy type.
Examples, tanh (0.95 + io) = 0.73978 + i o.
tanh (0.9 + i ia>) = 0.72494 i 0.07614.
[77]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) =u + iv. Continued
* = 1.05
1.15
0.76159
0.00
0.78181
0.00
0.80050
0.00
0.81775
0.00
0.83365
0.00
0.05
0.76357
0.03293
0.78368
0.03048
0.80227
0.02816
0.81943
0.02597
0.83522
0.02390
O.I
0.76950
0.06556
0.78932
0.06065
0.80760
0.05599
0.82444
0.05160
0.83992
0.04748
0.15
C77943
0.09757
0.79873
0.09016
0.81648
0.08317
0.83279
0.07658
0.84775
0.07041
0.2
0.79341
0.12858
0.81195
0.11867
0.82893
0.10932
0.84447
0.10054
0.85867
0.09233
0.25
0.81151
0.15821
0.82901
O.I4575
0.84495
0.13405
0.85945
0.12310
0.87264
0.1 1 288
-3
0.83377
0.18598
0.84991
0.17096
0.86450
0.15692
0.87768
0.14383
0.88958
0.13166
o-3S
0.86022
0.21133
0.87464
0.19377
0.88753
0.17742
0.89907
0.16226
0.90938
0.14823
0.4
0.89086
0.23361
0.903 1 1
0.21356
0.91392
0.19501
0.9234S
0.17789
0.93186
0.16213
o-45
0.92554
0.25205
o.935i5
0.22966
o.94344
0.20906
0.95058
0.19017
0.95674
0.17287
o-5
0.96403
0.26580
0.97045
0.24130
0.97574
0.21892
0.98010
0.19852
0.98368
0.17996
o-SS
1.00585
0.27392
1.00852
0.24767
1.01034
0.22389
1.01151
0.20236
1.01217
0.18288
0.6
1.05030
0.27542
1 .04864
0.24798
1.04654
0.22331
1-04415
0.20115
1. 04 1 60
0.18123
0.65
1.09632
0.26933
1 .08984
0.24144
1.08342
0.21658
1.07718
0.19441
1.07119
0.1 7461
0.7
1.14516
0.25486
1. 13084
0.22747
1.1 1984
0.20326
1. 10957
0.18182
1. 10003
0.16281
o.75
1.18715
0.23145
1. 17009
0.20572
1. 1 5445
0.18315
1.14015
0.16330
1. 12709
0.14580
0.8
1. 22812
0.19904
1.20585
0.17623
1-18575
0.15637
1. 16763
0.13002
1.15129
0.12380
0.85
1. 26319
0.15812
1.23624
O.I3955
1.21219
0.12347
1. 19346
0.10950
1.17152
0.09730
0.9
1. 29017
0.10993
1.25949
0.09677
1. 23231
0.08544
1. 20821
0.07563
1. 1 8680
0.06709
0.9S
1.30721
0.05638
1. 27410
0.04956
1.24492
0.04369
1.21914
0.03863
1.19631
0.03424
1.0
1 -3 x 304
0.00
1.27908
0.00
1.24922
0.00
1.22286
0.00
1. 19954
0.00
1.05
1-30721
0.05638
1. 27410
0.04956
1.24492
0.04369
1.21914
0.03863
1.19631
0.03424
1.1
1. 29017
0.10993
1.25949
0.09677
1. 23231
0.08544
1. 2082 1
0.07563
1. 1 8680
0.06709
i-i5
1. 26319
0.15812
1.23624
O.I3955
1.21219
0.12347
I.I9346
0.10950
1.17152
0.09730
1.2
1. 22812
0.19904
1.20585
0.17623
1-18575
0.15637
1. 16763
0.13902
1.15129
0.12380
1.25
1.18715
0.2314s
1. 17009
0.20572
I.I5445
0.18315
1.14015
0.16330
1. 12709
0.14580
i-3
1.14516
0.25486
1. 1 3084
0.22747
1.11984
0.20326
1. 10957
0.18182
1. 10003
0.1 628 1
1-35
1.09632
0.26933
1.08984
0.24144
1.08342
0.21658
1.07718
0.19441
1.07119
0.17461
1.4
1.05030
0.27542
1.04864
0.24798
1.04654
0.22331
1-04415
0.20115
1. 04 1 60
0.18123
i-4S
1.00585
0.27392
1.00852
0.24767
1. 01034
0.22389
1.01151
0.20236
1.01217
0.18288
i-5
0.96403
0.26580
0.97045
0.24130
0-97574
0.21892
0.98010
0.19852
0.98368
0.17996
i-55
0.92554
0.25205
o.935i5
0.22966
0.94344
0.20906
0.95058
0.19017
0.95674
0.17287
1.6
0.89086
0.23361
0.903 1 1
0.21356
0.91392
0.19501
0.92345
0.17789
0.93186
0.16213
1.65
0.86022
0.21133
0.87464
0.19377
0.88753
0.17742
0.89907
0.16226
0.90938
0.14823
i-7
0.83377
0.18598
0.84991
0.17096
0.86450
0.15692
0.87768
0.14383
0.88958
0.13166
i-75
0.81151
0.15821
0.82901
O.I4575
0.84495
0.13405
0.85945
0.12310
0.87264
0.1 1288
1.8
0.79341
0.12858
0.81195
0.11867
0.82893
0.10932
0.84447
0.10054
0.85867
0.09233
1.85
o.77943
0.09757
0.79873
0.09016
0.81648
0.08317
0.83279
0.07658
0.84775
0.07041
1.9
0.76950
0.06556
0.78932
0.06065
0.80760
0.05599
0.82444
0.05160
0.83992
0.04748
i-9S
0.76357
0.03293
0.78368
0.03048
0.80227
0.02816
0.81943
0.02597
0.83522
0.02390
2.0
0.76159
0.00
0.78181
0.00
0.80050
0.00
0.81775
0.00
0.83365
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (1.2 + i 0.75) = 1. 12709 4- i 0.14580.
tanh (1.2 + i 1.25) = 1. 12709 i 0.14580.
[78]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) - u + iv. Continued
x = 1.25
* = 1.3
* = i-35
x = 1.4
x = 1.45
0.84828
0.00
0.86172
0.00
0.87405
0.00
0.88535
0.00
0.89569
0.00
0.05
0.84975
0.02197
0.86309
0.02017
0.87533
0.01849
0.88653
0.01693
0.89678
0.01549
O.I
0.85414
0.04363
0.86719
0.04003
0.87913
0.03668
0.89006
0-03357
0.90005
0.03070
0.15
0.86145
0.06464
0.87398
0.05927
0.88544
0.05428
0.89591
0.04965
0.90545
0.04537
0.2
0.87162
0.08468
0.88344
0.07756
0.89421
0.07097
0.90401
0.06486
0.91293
0.05923
0.25
0.88461
0.10339
0.89548
0.09458
0.90535
0.08644
0.91429
0.07892
0.92240
0.07199
o-3
0.90032
0.12039
0.90791
0.10997
0.91875
0.10036
0.92663
0.09151
0.93375
0.08338
o.35
0.91861
0.13528
0.92686
0.12336
0.93425
0.1 1 240
0.94087
0.10234
0.94680
0.09312
0.4
0.93928
0.14765
0.94585
O.I3437
0.95166
0.12221
0.95680
0.11108
0.96137
0.10092
0-4S
0.96207
0.15706
0.96669
0.14262
0.97069
0.12945
0.97417
0.1 1 745
0.97719
0.10654
0.5
0.98661
0.16307
0.98903
0.14773
0.99101
0.13381
0.99263
0.12117
0.99396
0.10971
o.55
1. 01 244
0.16528
1. 01 243
O.I4937
1.01219
O.I3499
1.01181
0.1 2 199
1.01133
0.11026
0.6
1.03897
0.16332
1.03634
0.14722
1 -033 75
0.13275
1. 03 1 25
0.11972
1.02885
0.10801
0.65
1.06550
0.15691
1. 060 1 3
0.14109
1.05510
0.12693
1.05042
0.11425
1.04607
0.10288
0.7
1.09121
0.14591
1.08308
0.13088
1.07560
0.1 1 749
1.06875
0.10555
1.06248
0.09488
0-7S
1.11521
0.13034
1. 10439
0.11665
1.09457
0.10450
1.08565
0.09371
1.07756
0.0841 1
0.8
1. 13656
0.1 1042
1. 12328
0.09862
1.11131
0.08820
1. 10052
0.07896
1.09078
0.07077
0.85
I-IS434
0.08662
1-13895
0.07724
1.12512
0.06897
1.11277
0.06167
1.10166
0.05521
0.9
1. 16772
0.05964
1-15070
0.0531 1
i-i355i
0.04738
1.12192
0.04232
1. 10976
0.03785
-95
1. 17603
0.03041
I-I5799
0.02706
1.14192
0.02412
1. 12758
0.02153
1.11476
0.01925
1.0
1. 17885
0.00
1. 16047
0.00
1.14410
0.00
1. 1 2950
0.00
I.I 1646
0.00
1. 05
1.1 7603
0.03041
I-I5799
0.02706
1.14192
0.02412
1. 12758
0.02153
1.11476
0.01925
1.1
1. 16772
0.05964
1. 15070
0.05311
I-I355I
0.04738
1.12192
0.04232
I. 109 76
0.03785
1-15
i- 1 5434
0.08662
1-13895
0.07724
1.12512
0.06897
1.11277
0.06167
1.10166
0.05521
1.2
1. 13656
0.1 1042
1. 12328
0.09862
1.11131
0.08820
1. 10052
0.07896
1.09078
0.07077
1-25
1.11521
0.13034
1. 10439
0.11665
1.09457
0.10450
1.08565
0.09371
1.07756
0.0841 1
i-3
1.09121
0.14591
1.08308
0.13088
1.07560
0.1 1 749
1.06875
0.10555
1.06248
0.09488
i-35
1.06550
0.15691
1. 060 1 3
0.14100
1.05510
0.12693
1.05042
0.11425
1.04607
0.10288
1.4
1.03897
0.16332
1.03634
0.14722
I-Q3375
0.1327S
1.03 1 25
0.11972
1.02885
0.10801
1-45
1. 01 244
0.16528
1. 01 243
0.14937
1.01219
0.13499
1.01181
0.12199
1.01133
0.11026
i-5
0.98661
0.16307
. 0.98903
0.14773
0.99101
0.13381
0.99263
0.12117
0.99396
0.1 097 1
i-55
0.96207
0.15706
0.96669
0.14262
0.97069
0.12945
0.97417
O.I7745
0.97719
0.10654
1.6
0.93928
0.14765
0.94585
0.13437
0.95166
0.12221
0.95680
0.1 1 108
0.96137
0.10092
1.65
0.91861
0.13528
0.92686
0.12336
0.93425
0.11240
0.94087
0.10234
0.94680
0.09312
i-7
0.90032
0.12039
0.90791
0.10997
0.91875
0.10036
0.92663
0.09151
o-93375
0.08338
i-75
0.88461
0.10339
0.89548
0.09458
0.90535
0.08644
0.91429
0.07892
0.92240
0.07199
1.8
0.87162
0.08468
0.88344
0.07756
0.89421
0.07097
0.90401
0.06486
0.91293
0.05923
1.85
0.86145
0.06464
0.87398
0.05927
0.88544
0.05428
0.89591
0.04965
0.90545
0.04537
1.9
0.85414
0.04363
0.86719
0.04003
0.87913
0.03668
0.89006
0.03357
0.90005
0.03070
i-9S
0.84975
0.02197
0.86309
0.02017
0.87533
0.01849
0.88653
0.01693
0.89678
0.01549
2.0 0.84828 0.00
0.86172 0.00
0.87405 0.00
0.88535 0.00
0.89569 0.00
Note. Negative quantities are in heavy type.
Examples, tanh (1.4 + x<x8) = 1. 10052 + i 0.07896.
tanh (1.3 + irj) = 1.08308 i 0.13088.
[79]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) - u + iv. Continued
x = 1.5
x = 1-55
* = 1.6
x = 1.65
* = 1.7
0.90515
0.00
0.91379
0.00
0.92167
0.00
0.92886
0.00
o.9354i
0.00
0.05
0.90616
0.01415
0.91471
0.01292
0.92253
0.01178
0.92964
0.01074
0.93613
0.00979
O.I
0.90917
0.02804
0.91749
0.02560
0.92508
0.02334
0.93199
0.02127
0.93828
0.01937
0.15
0.91415
0.04143
0.92208
0.03779
0.92929
0.03445
0.93586
0.03138
0.94183
0.02857
0.2
0.92104
0.05404
0.92842
0.04927
o-935i 1
0.04488
0.941 19
0.04086
0.94671
0.03718
0.25
0.92975
0.06563
0.93641
0.05978
0.94245
0.05442
0.94791
0.04951
0.95285
0.04502
o-3
0.94017
0.07593
0-9459S
0.06909
0.95 1 18
0.06284
0.95589
0.05712
0.96015
0.05190
o-3S
0.95212
0.08468
0.95689
0.07697
0.961 1 7
0.06993
0.96501
0.06351
0.96846
0.05766
0.4
0.96542
0.09165
0.96903
0.08320
0.97223
0.07551
0.97509
0.06850
0.97763
0.06213
0-4S
0.97983
0.09660
0.98214
0.08758
0.98415
0.07938
0.98592
0.07193
0.98748
0.06517
o-5
0.99506
0.09933
0-99595
0.08992
0.99668
0.08139
0.99728
0.07367
0.99777
0.06667
o-55
1.01076
0.09965
1.01016
0.09008
1.00954
0.08142
1. 0089 1
0.07361
1.00829
0.06655
0.6
1.02657
0.09746
1. 02441
0.08796
1.02240
0.07940
1.02052
0.07169
1.01877
0.06474
0.65
1.04204
0.09268
1.03834
0.08353
1.03492
0.07530
1-03179
0.06791
1.02892
0.06126
0.7
1-05675
0.08534
1-05152
0.07680
1.04676
0.06915
1.04242
0.06230
1.03847
0.05614
0-7S
1.07022
0.07554
1.06357
0.06790
I-05755
0.06107
1.05209
0.05495
1. 047 14
0.04948
0.8
1.08200
0.06349
1.07408
0.05700
1.06693
0.05 1 21
1 .06049
0.04604
1.05466
0.04142
0.85
1.09167
0.04947
1.08269
0.04438
1. 07461
0.03984
1.06734
0.03579
1.06079
0.03218
0.9
1.09886
0.03390
1.08909
0.03038
1 .08030
0.02726
1.07241
0.02448
1-06533
0.02200
o-95
1. 10329
0.01723
1.09302
0.01544
1.08380
0.01385
1-07554
0.01243
1. 068 1 1
0.01117
1.0
1. 10479
0.00
1.09436
0.00
1.08500
0.00
1.07659
0.00
1.06906
0.00
1. 05
1. 10329
0.01723
1.09302
0.01544
1.08380
0.01385
I-Q7554
0.01243
1. 068 1 1
0.01117
1.1
1.09886
0.03390
1.08909
0.03038
1.08030
0.02726
1.07241
0.02448
1-06533
0.02200
i-i5
1.09167
0.04947
1.08269
0.04438
1. 0746 1
0.03984
1.06734
0.03579
1.06079
0.03218
1.2
1.08200
0.06349
1.07408
0.05700
1.06693
0.05121
1.06049
0.04604
1.05466
0.04142
1.25
1.07022
0.07554
1.06357
0.06790
1-05755
0.06107
1.05209
0.05495
1. 047 14
0.04948
i-3
1.05675
0.08534
1.05152
0.07680
1.04676
0.06915
1.04242
0.06230
1.03847
0.05614
*-3S
1.04204
0.09268
1.03834
0.08353
1.03492
0.07530
1. 03 1 79
0.06791
1.02892
0.06126
1.4
1.02657
0.09746
1. 02441
0.08796
1.02240
0.07940
1.02052
0.07169
1.01877
0.06474
i-4S
1.01076
0.09965
1.01016
0.09008
1.00954
0.08142
1. 0089 1
0.07361
1.00829
0.06655
i-5
0.99506
0.09933
0-99595
0.08992
0.99668
0.08139
0.99728
0.07367
0.99777
0.06667
i-55
0.97983
0.09660
0.98214
0.08758
0.98415
0.07938
0.98592
0.07193
0.98748
0.06517
1.6
0.96542
0.09165
0.96903
0.08320
0.97223
0.07551
0.97509
0.06850
0.97763
0.06213
1.6S
0.95212
0.08468
0.95689
0.07697
0.961 1 7
0.06993
0.96501
0.06351
0.96846
0.05766
i-7
0.94017
0.07593
Q-94595
0.06909
0.95 1 18
0.06284
0.95589
0.05712
0.96015
0.05190
i-75
0.92975
0.06563
0.93641
0.05978
0.94245
0.05442
0.94791
0.04951
0.95285
0.04502
1.8
0.92104
0.05404
0.92842
0.04927
o.935i 1
0.04488
0.941 19
0.04086
0.94671
0.03718
1. 8 5
0.91415
0.04143
0.92208
0.03779
0.92929
0.03445
0.93586
0.03138
0.94183
0.02857
1.9
0.90917
0.02804
0.91749
0.02560
0.92508
0.02334
0.93199
0.02127
0.93828
0.01937
1 -95
0.90616
0.01415
0.91471
0.01292
0.92253
0.01178
0.92964
0.01074
0.93613
0.00979
2.0
0.90515
0.00
0.91379
0.00
0.92167
0.00
0.92886
0.00
0-9354I
0.00
Note. Negative quantities are in heavy type.
Examples, tanh (1.7 + t'pj) = 1.03847 + * 0.05614.
tanh (1.6 + i 1.6) = 0.97223 i 0.07551.
[80]
Table IX. HYPERBOLIC TANGENTS, tanh {x + iq) = u + iv. Continued
x = i. 75
1.8
* = 1.85
* = 1.9
x = 1.95
0.94138
0.00
0.94681
0.00
o.95i75
0.00
0.95624
0.00
0.96032
0.00
0.05
0.94204
0.00891
0.94741
0.008 1 1
0.95230
0.00737
0.95674
0.00670
0.96078
0.00609
O.I
0.94400
0.01763
0.94921
0.01604
0-95394
0.01459
0.95825
0.01326
0.96215
0.01204
0.15
0.94725
0.02600
0.95218
0.02364
0.95666
0.02149
0.96072
0.01952
0.96441
0.01773
0.2
0.95172
0.03382
0.95626
0.03074
0.96038
0.02793
0.96412
0.02537
0.96750
0.02303
0.25
0-95733
0.04092
0.96139
0.03718
0.96506
0.03376
0.96838
0.03065
0.97138
0.02782
o-3
0.96399
0.04714
0.96746
0.04280
0.97059
0.03885
0.97342
0.03525
0-97597
0.03198
o-35
0.97156
0.05233
0-97435
0.04748
0.97686
0.04307
0.97912
0.03905
0.08116
0.03541
0.4
0.97991
0.05634
0.98194
0.05107
0.98376
0.04629
0.98538
0.04195
0.98684
0.03801
0-4S
0.98884
0.05904
0.99005
0.05348
0.991 1 1
0.04843
0.99206
0.04386
0.99289
0.03972
o-5
0.99818
0.06034
0.99851
0.05461
0.99878
0.04942
0.99900
0.04472
0.99918
0.04047
o-5S
1.00769
0.06017
1. 007 1 1
0.05440
1.00656
0.04919
1.00604
0.04448
1.00555
0.04022
0.6
1.01714
0.05848
1-01565
0.05283
1.01427
0.04773
1. 01300
0.04313
1. 01 184
0.03897
0.65
1.02629
0.05528
1.02389
0.04989
1.02170
0.04504
1.01970
0.04067
1.01788
0.03673
0.7
1.03488
0.05061
1.03162
0.04564
1.02866
0.041 18
1.02596
0.03716
1.02352
0.03354
0-7S
1.04266
0.04457
1. 0386 1
0.04016
1.03494
0.03621
1.03162
0.03265
1.02862
0.02946
0.8
1.04940
0.03729
1 .04466
0.03358
1.04037
0.03026
1.03650
0.02727
1.03300
0.02459
0.85
1.05489
0.02895
1.04958
0.02606
1.04478
0.02347
1 .04046
0.02115
1.03656
0.01906
0.9
1.05895
0.01978
1.05320
0.01780
1 .04804
0.01602
I-04337
0.01443
1. 039 1 8
0.01301
o-95
1.06 143
0.01004
i-o5543
0.00903
1.05003
0.00813
1.045 16
0.00732
1.04078
0.00659
1.0
1.06228
0.00
1.05619
0.00
1.05070
0.00
1.04576
0.00
1.04131
0.00
1.05
1. 06 143
0.01004
I-05543
0.00903
1.05003
0.00813
1.045 16
0.00732
1.04078
0.00659
1.1
1.05895
0.01978
1.05320
0.01780
1.04804
0.01602
1 -0433 7
0.01443
1. 039 1 8
0.01301
I.I5
1.05489
0.02895
1.04958
0.02606
1.04478
0.02347
1.04046
0.02115
1.03656
0.01906
1.2
1.04940
0.03729
1 .04466
0.03358
1.04037
0.03026
1.03650
0.02727
1.03300
0.02459
1.25
1.04266
0.04457
1.03861
0.04016
1.03494
0.03621
1.03162
0.03265
1.02862
0.02946
i-3
1.03488
0.05061
1. 03 1 62
0.04564
1.02866
0.041 18
1.02596
0.03716
1.02352
0.03354
i-3S
1.02629
0.05528
1.02389
0.04989
1. 02 1 70
0.04504
1.01970
0.04067
1.01788
0.03673
1.4
1.01714
0.05848
1.01565
0.05283
1.01427
0.04773
1.01300
0.04313
1.01184
0.03897
1 -45
1.00769
0.06017
1.00711
0.05440
1.00656
0.04919
1.00604
0.04448
1-00555
0.04022
i-5
0.99818
0.06034
0.99851
0.05461
0.99878
0.04942
0.99900
0.04472
0.99918
0.04047
i-5S
0.98884
0.05904
0.99005
0.05348
0.991 1 1
0.04843
0.99206
0.04386
0.99289
0.03972
1.6
0.97991
0.05634
0.98194
0.05107
0.98376
0.04629
0.98538
0.04195
0.98684
0.03801
1.65
0.97156
0.05233
0-97435
0.04748
0.97686
0.04307
0.97912
0.03905
0.981 16
0.03541
i-7
0.96399
0.04714
0.96746
0.04280
0.97059
0.03885
0.97342
0.03525
o.97597
0.03198
i-75
0-95733
0.04092
0.96139
0.03718
0.96506
0.03376
0.96838
0.03065
0.97138
0.02782
1.8
0.95172
0.03382
0.95626
0.03074
0.96038
0.02793
0.96412
0.02537
0.96750
0.02303
i.8 S
0.94725
0.02600
0.95218
0.02364
0.95666
0.02149
0.96072
0.01952
0.96441
0.01773
1.9
0.94400
0.01763
0.94921
0.01604
0-9S394
0.01459
0.95825
0.01326
0.96215
0.01204
1 -95
0.94204
0.00891
0.94741
0.0081 1
0.95230
0.00737
0.95674
0.00670
0.96078
0.00609
2.0
0.94138
0.00
0.94681
0.00
o.95i75
0.00
0.95624
0.00
0.96032
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (1.85 4-
i 0.85) =
1.04478 4- i 0.02347.
tanh (1.95 + i 1.25) = 1.02862 i 0.02946.
[81]
Table IX. HYPERBOLIC TANGENTS, tanh (* + iq) =u+ iv. Continued
X = 2.0S
x = 2.15
0.96403
0.00
0.96740
0.00
0.97045
0.00
0.97323
0.00
o.97574
0.00
0.05
0.96445
0.00553
0.96778
0.00502
0.97080
0.00456
o.97354
0.00413
0.97603
0.00375
O.I
0.96570
0.01094
0.96892
0.00993
0.97184
0.00901
o.97449
0.00817
0.97689
0.00741
0.15
0.96775
0.01610
0.97079
0.01461
o.97354
0.01326
0.97604
0.01203
0.97830
0.01091
0.2
0.97058
0.02090
0.97336
0.01897
0.97588
0.01721
0.97816
0.01561
0.98023
0.01415
0.25
0.9741 1
0.02524
0.97657
0.02289
0.97880
0.02076
0.98081
0.01882
0.98264
0.01706
-3
0.97827
0.02900
0.98036
0.02630
0.98224
0.02384
0.98394
0.02161
0.98548
0.01958
o-3S
0.98299
0.03209
0.98464
0.02909
0.98613
0.02636
0.98747
0.02388
0.98868
0.02163
0.4
0.98815
0.03444
0.98932
0.03120
0.99037
0.02826
0.99132
0.02559
0.99217
0.02317
0-4S
0.99364
0.03596
0.99430
0.03256
0.99489
0.02948
0.99541
0.02669
0.99587
0.02416
o-5
0-99933
0.03662
0.99945
0.03314
0-99955
0.02998
0.99963
0.02713
0.99970
0.02455
o-55
1.00509
0.03638
1.00466
0.03290
1.00426
0.02976
1.00389
0.02691
1-00355
0.02434
0.6
1.01077
0.03523
1.00979
0.03184
1.00890
0.02878
1 .00808
0.02602
1.00734
0.02353
0.65
1.01623
0.03318
1.01471
0.02998
I-OI334
0.02709
1.01210
0.02448
1.01097
0.02212
0.7
1.02131
0.03028
1.01930
0.02734
1. 01 748
0.02469
1-01583
0.02231
1. 01434
0.02015
o-7S
1.02589
0.02658
1.02343
0.02399
1.02120
0.02166
1.01919
0.01956
1. 01 736
0.01767
0.8
1.02984
0.02218
1.02698
0.02001
1.02440
0.01806
1.02207
0.01631
1. 01 996
0.01472
0.85
1.03304
0.01719
1.02986
0.01550
1.02699
0.01399
1.02440
0.01262
1.02206
0.0 1 140
0.9
I-Q3539
0.01172
1.03197
0.01057
1.02889
0.00954
1.02611
0.00861
1.02360
0.00777
o-9S
1.03683
0.00594
1.03327
0.00536
1.03005
0.00483
1.02715
0.00436
1.02454
0.00394
1.0
1-03731
0.00
1.03370
0.00
1.03045
0.00
1.02751
0.00
1.02486
0.00
1. 05
1.03683
0.00594
1.03327
0.00536
1.03005
0.00483
1.02715
0.00436
1.02454
0.00394
1.1
1-03539
0.01172
1-03197
0.01057
1.02889
0.00954
1.02611
0.00861
1.02360
0.00777
Ms
1.03304
0.01719
1.02986
0.01550
1.02699
0.01399
1.02440
0.01262
1.02206
0.01140
1.2
1.02984
0.02218
1.02698
0.02001
1.02440
0.01806
1.02207
0.01631
1.01996
0.01472
1-25
1.02589
0.02658
1.02343
0.02399
1. 02 1 20
0.02166
1.01919
0.01956
1. 01736
0.01767
i-3
1. 02 13 1
0.03028
1. 01 930
0.02734
1. 01 748
0.02469
1.01583
0.02231
1. 01434
0.02015
i-3S
1.01623
0.03318
1.01471
0.02998
I-OI334
0.02709
1.01210
0.02448
1.91097
0.02212
1.4
1.01077
0.03523
1.00979
0.03184
1.00890
0.02878
1 .00808
0.02602
1.00734
0.02353
1. 45
1.00509
0.03638
1.00466
0.03290
1.00426
0.02976
1.00389
0.02691
1-00355
0.02434
i-S
0-99933
0.03662
0.99945
0.03314
0-99955
0.02998
0.99963
0.02713
0.99970
0.02455
i-5S
0.99364
0.03596
0.99430
0.03256
0.99489
0.02948
0.99541
0.02669
0.99587
0.02416
1.6
0.98815
0.03444
0.98932
0.03120
0.99037
0.02826
0.99132
0.02559
0.99217
0.02317
1.65
0.98299
0.03209
0.98464
0.02909
0.98613
0.02636
0.98747
0.02388
0.98868
0.02163
i-7
0.97827
0.02900
0.98036
0.02630
0.98224
0.02384
0.98394
0.02161
0.98548
0.01958
i-75
0.9741 1
0.02524
0.97657
0.02289
0.97880
0.02076
0.98081
0.01882
0.98264
0.01706
1.8
0.97058
0.02090
0.97336
0.01897
0.97588
0.01721
0.97816
0.01561
0.98023
0.01415
1.85
0.96775
0.01610
0.97079
0.01461
o.97354
0.01326
0.97604
0.01203
0.97830
0.01091
1.9
0.96570
0.01094
0.96892
0.00993
0.97184
0.00901
o.97449
0.00817
0.97689
0.00741
i-95
0.96445
0.00553
0.96778
0.00502
0.97080
0.00456
0.97354
0.00413
0.97603
0.00375
2.0
0.96403
0.00
0.96740
0.00
0.97045
0.00
0.97323
0.00
0.97574
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (2.2 4-
i 0) =0 9;
7574 + *o.
tanh (2.15 4- i 1.15) = 1.02440 i 0.01262.
[82]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) = u + iv. Continued
x = 2.25
x = 2.3
x 2.35
x = 2.4
x = 2.45
0.97803
0.00
0.98010
0.00
0.98197
0.00
0.98367
0.00
0.98522
0.00
0.0s
0.97829
0.00340
0.98034
0.00308
0.98219
0.00280
0.98387
0.00253
0.98540
0.00230
O.I
0.97907
0.00672
0.98105
0.00610
0.98283
0.00553
0.98446
0.00501
0.98592
0.00454
0.15
0.98035
0.00989
0.98221
0.00897
0.98389
0.00813
0.98541
0.00736
0.98680
0.00667
0.2
0.98210
0.01283
0.98380
0.01163
0.98534
0.01054
0.98673
0.00955
0.98799
0.00865
0.25
0.98429
0.01547
0.98579
0.01401
0.98714
0.01270
0.98836
0.01150
0.98947
0.01042
-3
0.98687
0.01774
0.98813
0.01607
0.98926
0.01456
0.99029
0.01319
0.99121
0.01194
o-3S
0.98977
0.01960
0.99076
0.01775
0.99165
0.01607
0.99245
0.01456
0.99317
0.01318
0.4
0.99294
0.02098
0-99363
0.01900
0.99425
0.01720
0.99481
0.01557
o.9953i
0.01410
0.45
0.99629
0.02187
0.99667
0.01979
0.99700
0.01791
0.99730
0.01621
0-99757
0.01468
o-S
C99975
0.02222
0.99980
0.02010
0.99984
0.01819
0.99986
0.01646
0.99989
0.01489
0-5S
1.00324
0.02202
1.00295
0.01992
1.00269
0.01802
1.00245
0.01630
1.00222
0.01474
0.6
1.00666
0.02127
1.00604
0.01924
1.00549
0.01740
1.00498
0.01573
1. 0045 1
0.01423
0.65
1.00994
0.02000
1.00900
0.01808
1.00816
0.01634
1.00739
0.01478
1.00693
0.01336
0.7
1. 01 298
0.01821
1.01175
0.01646
1.01064
0.01487
1 .00963
0.01345
1.00872
0.01216
0-7S
1.01571
0.01596
1.01421
0.01442
1. 01 286
0.01303
1. 01 164
0.01178
1-01053
0.01064
0.8
1. 01 805
0.01330
1.01632
0.01201
1.01477
0.01085
1.01336
0.00981
1. 01 208
0.00886
0.85
1. 01 994
0.01029
1. 01 803
0.00929
1.01631
0.00839
1.01475
0.00758
1-01333
0.00685
0.9
1.02133
0.00701
1.01928
0.00633
1.01744
0.00572
1.01576
0.00517
1.01425
0.00467
o-95
1.02218
0.00355
1.02006
0.00322
1.01812
0.00290
1.01639
0.00262
1.01482
0.00237
1.0
1.02247
0.00
1. 0203 1
0.00
1.01836
0.00
1.01659
0.00
1.01500
0.00 .
1.05
1.02218
0.00355
1.02006
0.00322
1.01812
0.00290
1.01639
0.00262
1.01482
0.00237
1.1
1-02133
0.00701
1.01928
0.00633
1. 01 744
0.00572
1.01576
0.00517
1-01425
0.00467
r.15
1. 01 994
0.01029
1. 01803
0.00929
1.01631
0.00839
1.01475
0.00758
1-01333
0.00685
1.2
1. 01 805
0.01330
1. 0163 2
0.01201
1.01477
0.01085
1.01336
0.00981
1. 01 208
0.00886
1.25
1.01571
0.01596
1.01421
0.01442
1.01286
0.01303
1.01164
0.01178
1-01053
0.01064
i-3
1. 01 298
0.01821
1.01175
0.01646
1. 01064
0.01487
1.00963
0.01345
1.00872
0.01216
1-35
1.00994
0.02000
1.00900
0.01808
1. 008 1 6
0.01634
1.00739
0.01478
1.00693
0.01336
1.4
1.00666
0.02127
1 .00604
0.01924
1.00549
0.01740
1.00498
0.01573
1. 0045 1
0.01423
1 45
1.00324
0.02202
1.00295
0.01992
1.00269
0.01802
1.00245
0.01630
1.00222
0.01474
i-5
0-99975
0.02222
0.99980
'0.02010
0.99984
0.01819
0.99986
0.01646
0.99989
0.01489
i-55
0.99629
0.02187
0.99667
0.01979
0.99700
0.01791
0.99730
0.01621
o.99757
0.01468
1.6
0.99294
0.02098
0.99363
0.01900
0.99425
0.01720
0.99481
0.01557
0-9953I
0.01410
1.65
0.98977
0.01960
0.99076
0.01775
0.99165
0.01607
0.99245
0.01456
0.99317
0.01318
i-7
0.98687
0.01774
0.98813
0.01607
0.98926
0.01456
0.99029
0.01319
0.99121
0.01194
i-7S
0.98429
0.01547
0.98579
0.01401
0.98714
0.01270
0.98836
0.01150
0.98947
0.01042
1.8
0.98210
0.01283
0.98380
0.01163
0.98534
0.01054
0.98673
0.00955
0.98799
0.00865
1. 8 5
0.98035
0.00989
0.98221
0.00897
0.98389
0.00813
0.98541
0.00736
0.98680
0.00667
1.9
0.97907
0.00672
0.98105
0.00610
0.98283
0.00553
0.98446
0.00501
0.98592
0.00454
i-95
0.97829
0.00340
0.98034
0.00308
0.98219
0.00280
0.98387
0.00253
0.98540
0.00230
2.0
0.97803
0.00
0.98010
0.00
0.98197
0.00
0.98367
0.00
0.98522
0.00
Note. Negative quantities are in heavy type.
Examples, tanh (2.25 + i 0.25) = 0.98429 + i 0.01547.
tanh (2.45 + i 1.45) = 1.00222 i 0.01474.
[83J
Table IX. HYPERBOLIC TANGENTS, tanh {x + iq) = u + iv. Continued
x = 2.5
x = 2.55
* = 2.6
X = 2.6
x = 2.7
0. 8661
0.00
0.98788
0.00
0.98903
0.00
0.99007
0.00
0.99101
0.00
0.05
0.98678
0.00208
0.98803
0.00189
0.98916
0.00171
0.99019
0.00155
0.991 1 2
0.00140
O.I
0.98726
0.0041 1
0.98846
0.00373
0.98956
0.00337
0-99055
0.00306
0.99144
0.00277
0.15
0.98805
0.00605
0.98918
0.00548
0.99021
0.00496
0.991 13
0.00449
0.99198
0.00407
0.2
0.98913
0.00784
0.99016
0.00710
0.99109
0.00643
0.99194
0.00582
0.99270
0.00527
0.25
0.99047
0.00944
0.99138
0.00855
0.99220
0.00774
0.99294
0.00701
0.99361
0.00635
o-3
0.99205
0.01082
0.99281
0.00979
0.99350
0.00887
0.99412
0.00803
0.99468
0.00727
o-3S
o-99383
0.01193
0.99442
0.01080
0.99495
0.00978
0.99544
0.00886
0.99588
0.00802
0.4
0.99576
0.01276
0.99617
0.01155
0.99654
0.01046
0.99688
0.00947
0.99718
0.00857
0-4S
0.99781
0.01328
0.99802
0.01202
0.99822
0.01088
0.99839
0.00985
o-99855
0.00891
o-5
0.99991
0.01348
0.99993
0.01219
0.99994
0.01103
0.99995
0.00998
0.99996
0.00903
0-5S
1.00202
0.01334
1. 00 1 84
0.01207
1.00167
0.01092
1.00151
0.00988
1.00137
0.00893
0.6
1.00409
0.01287
1-00371
0.01164
1.00336
0.01053
1.00304
0.00952
1.00276
0.00862
0.65
1.00606
0.01208
1.00549
0.01093
1 .00498
0.00988
1.00450
0.00894
1 .00408
0.00808
0.7
1.00789
0.01099
1.00714
0.00994
1.00647
0.00898
1.00585
0.00812
1.00530
0.00735
o.75
1.00953
0.00962
1.00862
0.00870
1.00780
0.00786
1.00706
0.00711
1.00639
0.00643
0.8
1. 01 093
0.00801
1.00989
0.00726
1.00895
0.00654
1 .00809
0.00592
1.00732
0.00535
o.8 S
1. 01 206
0.00619
1.01091
0.00560
1.00987
0.00506
1.00893
0.00457
1.00807
0.00413
0.9
1. 01 289
0.00422
1.01166
0.00381
1-01054
0.00345
1.00954
0.00312
1.00862
0.00282
o-9S
1. 01340
0.00214
1.0121,1
0.00193
1. 01 096
0.00175
1. 0099 1
.0.00158
1.00896
0.00143
1.0
1-01357
0.00
1.01227
0.00
I.OIIIO
0.00
1. 01003
0.00
1.00907-
0.00
1. 05
1-01340
0.00214
1.01211
0.00193
1. 01096
0.00175
1. 0099 1
0.00158
1.00896
0.00143
i.i
1. 01 289
0.00422
1.01166
0.00381
1.01054
0.00345
1.00954
0.00312
1.00862
0.00282
i-i5
1. 01 206
0.00619
1.01091
0.00560
1.00987
0.00506
1 .00893
0.00457
1.00807
0.00413
1.2
1 .01093
0.00801
1 .00989
0.00726
1.00895
0.00654
1 .00809
0.00592
1.00732
0.00535
1.25
1.00953
0.00962
1.00862
0.00870
1.00780
0.00786
1.00706
0.0071 1
1.00639
0.00643
i-3
1.00789
0.01099
1.00714
0.00994
1.00647
0.00898
1.00585
0.00812
1.00530
0.00735
1 -35
1.00606
0.01208
1.00549
0.01093
1 .00498
0.00988
1.00450
0.00894
1.00408
0.00808
1.4
1 .00409
0.01287
1-00371
0. 01 164
1.00336
0.01053
1 .00304
0.00952
1.00276
0.00862
i-4S
1.00202
0.01334
1.00184
0.01207
1.00167
0.01092
1.00151
0.00988
1.00137
0.00893
i-5
0.99991
0.01348
0-99993
0.01219
0.99994
0.01103
0.99995
0.00998
0.99996
0.00903
i-55
0.99781
0.01328
0.99802
0.01202
0.99822
0.01088
0.99839
0.00985
o-99855
0.00891
1.6
0.99576
0.01276
0.99617
0.01155
0.99654
0.01046
0.99688
0.00947
0.99718
0.00857
1.65
0.99383
0.01193
0.99442
0.01080
0-99495
0.00978
0-99544
0.00886
0.99588
0.00802
i-7
0.99205
0.01082
0.99281
0.00979
0-99350
0.00887
0.99412
0.00803
0.99468
0.00727
i-75
0.99047
0.00944
0.99138
0.00855
0.99220
0.00774
0.99294
0.00701
0.99361
0.00635
1.8
0.98913
0.00784
0.99016
0.00710
0.99109
0.00643
0.99194
0.00582
0.99270
0.00527
1.85
0.98805
0.00605
0.98918
0.00548
0.99021
0.00496
0.99113
0.00449
0.99198
0.00407
1.9
0.98726
0.0041 1
0.98846
0.00373
0.98956
0.00337
0-99055
0.00306
0.99144
0.00277
1 -95
0.98678
0.00208
0.98803
0.00189
0.98916
0.00171
0.99019
0.00155
0.99112
0.00140
2.0
0.98661
0.00
0.98788
0.00
0.98903
0.00
0.99007
0.00
0.99101
0.00
Note. Negative quantities are in heavy type.
Examples, tanh (2.60 + 0.35) = 0.99495 + * 0.00978.
tanh (2.70 + i 1.35) = 1.00408 i 0.00808.
[84]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) =u+ iv. Continued
o
0.05
O.I
0.15
0.2
0.25
-3
o-3S
0.4
0-4S
-5
o.55
0.6
0.65
0.7
0-7S
0.8
0.85
0.9
0.9S
1.0
1. 05
1.1
i-i5
1.2
1.25
i-3
i-35
1.4
i-45
i-5
i-55
1.6
1.65
i-7
i-75
1.8
1.8S
1.9
i-9S
x = 2.75
0.99186 0.00
0.99196 0.00127
0.99225 0.00251
0.99274 0.00368
0.99340 0.00477
0.99422 0.00575
0.99519 0.00658
0.99627 0.00726
0.99745 0.00775
0.99869 0.00806
0.99997 0.00817
1. 001 25 0.00808
1.00250 0.00779
1.00369 0.00731
1.00479 0.00664
1.00578 0.00581
1.00662 0.00484
1.00730 0.00374
1.00780 0.00255
1. 008 10 0.00129
1. 008 2 1 0.00
1.00810 0.00129
1.00780 0.0025s
1.00730 0.00374
1.00662 0.00484
1.00578 0.00581
1.00479 0.00664
1.00369 0.00731
1.00250 0.00779
1. 001 25 0.00808
0.99997 0.00817
0.99869 0.00806
0.99745 0.00775
0.99627 0.00726
0.99519 0.00658
0.99422 0.00575
0.99340 0.00477
0.99274 0.00368
0.99225 0.00251
0.99196 0.00127
0.99186 0.00
x = 2.80
0.99263 0.00
0.99272 0.00115
0.99299 0.00227
0.99343 0.00334
0.99403 0.00432
0.99477 0.00519
0.99564 0.00596
0.99663' 0.00657
0.99769 0.00702
0.99882 0.00730
0.99997 0.00740
1.00113 0.00731
1.00226 0.00705
1.00334 0.00661
1.00434 0.00601
1.00523 0.00525
1.00599 Q-00437
1. 0066 1 0.00338
1.00706 0.00230
1.00733 0.00117
1.00742 0.00
1.00733 0.00117
1.00706 0.00230
1. 0066 1 0.00338
1.00599 0.00437
1.00523 0.00525
1.00434 0.00601
1.00334 0.00661
1.00226 0.00705
1. 001 13 0.00731
0.99997 0.00740
0.99882 0.00730
0.99769 0.00702
0.99663 0.00657
0.99564 0.00596
0.99477 0.00519
0.99403 0.00432
0.99343 0.00334
0.99299 0.00227
0.99272 0.00115
0.99263 0.00
* = 2.85
0-99333 0.00
0.99341 0.00104
0.99365 0.00206
0.99405 0.00302
0.99459 0.00391
0.99527 0.00471
0.99606 0.00539
0.99695 0.00594
0.99791 0.00635
0.99893 0.00660
0.99998 0.00669
1. 00 1 03 0.00662
1.00205 0.00638
1.00303 0.00598
1.00393 0.00544
1.00473
1.00542
1.00598
1.00638
1.00663
1.00671
1.00663
1.00638
1.00598
1.00542
0.00475
0.00396
0.00306
0.00208
0.00105
0.00
o.oofos
0.00208
0.00306
0.00396
1.00473 0.00475
1.00393 0.00544
1.00303 0.00598
1.00205 0.00638
1. 00103 0.00662
0.99998 0.00669
0.99893 0.00660
0.99791 0.00635
0.99695 0.00594
0.99606 0.00539
0.99527 0.00471
0.99459 0.00391
0.99405 0.00302
0.99365 0.00206
0.99341 0.00104
0-99333 o-oo
x = 2.90
0.99396 0.00
0.99404 0.00094
0.99426 0.00186
0.99462 0.00273
0.9951 I 0.00354
0.99572 0.00426
0.99644 0.00488
0.99724 0.00538
0.9981 I 0.00575
0.99904 0.00598
0.99998 0.00606
1.00093 0.00599
1.00186 0.00577
1.00274 0.00541
1.00355 0.00480
1.00428 0.00430
1.00490 0.00358
1.00540 0.00276
1.00577 0.00188
1.00600 0.00095
1.00607
1.00600
1.00577
1.00540
1 .00490
1.00428
1 -003 5 5
1.00274
1.00186
1.00093
0.99998
0.99904
0.9981 1
0.99724
0.99644
0.99572
0.9951 1
0.99462
0.99426
0.99404
0.00
0.00095
0.00188
0.00276
0.00358
0.00430
0.00480
0.00541
0.00577
0.00599
0.00606
0.00598
0.00575
0.00538
0.00488
0.00426
0.00354
0.00273
0.00186
0.00094
0.99396 0.00
x = 2.95
0.99454 0.00
0.99460 0.00085
0.99480 0.00168
0.99513 0.00248
o-99557 0.00321
0.99613 0.00386
0.99678 0.00442
0.99750 0.00487
0.99830 0.00520
0.99913 0.00541
0.99999 0.00548
1.00084 0.00542
1. 00 1 68 0.00522
1.00248 0.00489
1.00322 0.00445
1.00387 0.00389
1.00444 0.00324
1.00489 0.00250
1.00522 0.00170
1.00542 0.00086
1.00549 0.00
1.00542 0.00086
1.00522 0.00170
1.00489 0.00250
1.00444 0.00324
1.00387 0.00389
1.00322 0.00445
1.00248 0.00489
1.00168 0.00522
1.00084 0.00542
0.99999 0.00548
0.99913 0.00541
0.99830 0.00520
0.99750 0.00487
0.99678 0.00442
0.99613 0.00386
0.99557 0.00321
0.99513 0.00248
0.99480 0.00168
0.99460 0.00085
0.99454 0.00
Note. Negative quantities are in heavy type.
Examples, tanh (2.9 + i 0.9) = 1.00577 + i 0.00188.
tanh (2.95 4- i 1.95) = 0.99460 i 0.00085.
[85]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) = u + iv. Continued
x = 3.0
* r 3-05
x - 3.10
x = 3. 15
x = 3.20
0-99505
0.00
o.99552
0.00
0-9959S
0.00
0.99633
0.00
0.99668
0.00
0.05
0.99512
0.00077
o.99558
0.00070
0.99600
0.00063
0.99638
0.00057
0.99672
0.00052
O.I
o.9953o
0.00153
o.99574
0.00138
0.99615
0.00125
0.99651
0.00113
0.99684
0.00102
0.15
o.99559
0.00224
0.99601
0.00203
0.99639
0.00184
0.99673
0.00166
0.99704
0.00150
0.2
0.99599
0.00290
0.99637
0.00263
0.99672
0.00238
0.99703
0.00215
0.99731
0.00195
0.2s
0.99649
0.00349
0.99683
0.00316
0.99713
0.00286
0.99740
0.00259
0.99765
0.00234
-3
0.99708
0.00400
0.99736
0.00362
0.99761
0.00328
0.99784
0.00297
0.99805
0.00268
o-3S
0.99774
0.00441
0.99796
0.00399
0.99815
0.00361
0.99833
0.00327
0.99849
0.00296
0.4
0.99846
0.00471
0.99861
0.00426
0.99874
0.00386
0.99886
0.00349
0.99897
0.00316
o.45
0.99921
0.00489
0.99929
0.00443
0.99936
0.00401
0.99942
0.00363
0-99947
0,00328
o-5
0.99999
0.00496
o.99999
0.00449
0.99999
0.00406
o.99999
0.00367
0.99999
0.00332
-55
1.00076
0.00490
1.00069
0.00443
1.00063
0.00401
1.00057
0.00363
1. 0005 1
0.00328
0.6
1.00152
0.00472
1.00138
0.00427
1.00125
0.00387
1.00113
0.00350
1.00102
0.00316
0.65
1.00224
0.00443
1.00203
0.00401
1.00184
0.00362
1. 00166
0.00328
1.00151
0.00297
0.7
1.00291
0.00402
1.00263
0.00364
1.00238
0.00329
1.00216
0.00298
1.00195
0.00269
o-75
1.00351
0.00352
1.00317
0.00318
1.00287
0.00288
1.00260
0.00260
1.00235
0.00236
0.8
1. 0040 1
0.00293
1.00363
0.00265
1.00329
0.00239
1.00297
0.00217 .
1.00269
0.00196
0.85
1.00443
0.00226
1 .00400
0.00205
1.00362
0.00185
1.00328
0.00167
1.00297
0.00151
0.9
1.00473
0.00154
1.00426
0.00139
1.00387
0.00126
1.00350
0.00114
1 .003 1 7
0.00103
o-9S
1. 0049 1
0.00078
1 .00444
0.00071
1 .00402
0.00064
1.00363
0.00058
1.00329
0.00052
1.0
1.00497
0.00
1.00450
0.00
1.00407
0.00
1.00368
0.00
1-00333
0.00
1.05
1. 0049 1
0.00078
1 .00444
0.00071
1.00402
0.00064
1.00363
0.00058
1.00329
0.00052
1.1
1.00473
0.00154
1.00426
0.00139
1.00387
0.00126
1.00350
0.00114
1.00317
0.00103
i-i5
1.00443
0.00226
1 .00400
0.00205
1.00362
0.00185
1.00328
0.00167
1.00297
0.00151
1.2
1. 0040 1
0.00293
1.00363
0.00265
1.00329
0.00239
1.00297
0.00217
1.00269
0.00196
1.25
1-00351
0.00352
1.00317
0.00318
1.00287
0.00288
1.00260
0.00260
1.00235
0.00236
i-3
1.00291
0.00402
1.00263
0.00364
1.00238
0.00329
1.00216
0.00298
1.00195
0.00269
i-3S
1.00224
0.00443
1.00203
0.00401
1.00184
0.00362
1.00166
0.00328
1.00151
0.00297
1.4
1.00152
0.00472
1.00138
0.00427
1.00125
0.00387
1.00113
0.00350
1.00102
0.00316
i-4S
1.00076
0.00490
1.00069
0.00443
1.00063
0.00401
1.00057
0.00363
1.0005 1
0.00328
i-5
0.99999
0.00496
0-99999
0.00449
o.99999
0.00406
o.99999
0.00367
0.99999
0.00332
i-S5
0.99921
0.00489
0.99929
0.00443
0.99936
0.00401
0.99942
0.00363
0.99947
0.00328
1.6
0.99846
0.00471
0.99861
0.00426
0.99874
0.00386
0.99886
0.00349
0.99897
0.00316
1.65
0.99774
0.00441
0.99796
0.00399
0.99815
0.00361
0.99833
0.00327
0.99849
0.00296
i-7
0.99708
0.00400
0.99736
0.00362
0.99761
0.00328
0.99784
0.00297
0.99805
0.00268
i-7S
0.99649
0.00349
0.99683
0.00316
0.99713
0.00286
0.99740
0.00259
0.99765
0.00234
1.8
0.99599
0.00290
0.99637
0.00263
0.99672
0.00238
0.99703
0.00215
0.99731
0.00195
1.8s
o.99559
0.00224
0.99601
0.00203
0.99639
0.00184
0.99673
0.00166
0.99704
0.00150
1.9
0.99530
0.00153
C99574
0.00138
0.99615
0.00125
0.99651
0.00113
0.99684
0.00102
1 -95
0.99512
0.00077
o.99558
0.00070
0.99600
0.00063
0.99638
0.00057
0.99672
0.00052
2.0
0.99505
0.00
o.99552
0.00
0-99595
0.00
0-99633
0.00
0.99668
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (3.0 4- i
1 .00) = ]
.00497 4-
to.
[86]
Table IX. HYPERBOLIC TANGENTS, tanh (x + iq) =u+ iv. Continued
x = 3-25
x = 3.30
x - 3-35
x = 3.40
3-45
0.99700
0.00
0.99728
0.00
o.99754
0.00
0.99777
O.OO
0.99799
0.00
0.05
0.99704
0.00047
0.99732
0.00042
o.99757
0.00038
0.99780
O.OOO35
0.99801
0.00031
O.I
0.99715
0.00093
0.99742
0.00084
0.99766
0.00076
0.99788
O.OO069
0.99809
0.00062
0.15
0.99732
0.00136
0.99758
0.00123
0.99781
0.00112
0.99802
O.OOIOI
0.99821
0.00091
0.2
o.99757
0.00176
0.99780
0.00160
0.99801
0.00144
0.99820
0.00131
0.99837
0.00118
0.25
0.99787
0.00212
0.99808
0.00192
0.99826
0.00174
0.99843
0.00157
0.99857
0.00142
o-3
0.98823
0.00243
0.99840
0.00220
o.99855
0.00199
0.99869
0.00180
0.99881
0.00163
0-35
0.99863
0.00268
0.99876
0.00242
0.99888
0.00219
0.99899
0.00198
0.99908
0.00179
0.4
0.99907
0.00286
0.99916
0.00259
0.99924
0.00234
0.99931
0.00212
0.99938
0.00192
0.45
Q-99953
0.00297
C99957
0.00269
0.99961
0.00243
0.99965
0.00220
0.99968
0.00200
-5
1. 00000
0.00301
1 .00000
0.00272
1. 00000
0.00246
1. 00000
0.00223
I. OOOOO
0.00202
.55
1.00047
0.00297
1.00042
0.00269
1.00038
0.00243
1.00035
0.00220
1 .0003 1
0.00200
0.6
1. 0009 1
0.00286
1 .00084
0.00259
1.00076
0.00234
1.00069
0.00212
1.00062
0.00192
0.65
1.00136
0.00268
1.00123
0.00243
1.00112
0.00220
I.OOIOI
0.00199
1. 0009 1
0.00180
0.7
1.00177
0.00244
1.00160
0.00220
1. 00145
0.00199
1.00131
0.00180
1.00118
0.00163
o.75
1.00213
0.00213
1.00192
0.00193
1. 001 74
0.00174
1.00158
0.00158
1. 00143
0.00143
0.8
1.00244
0.00177
1.00222
0.00160
1.00199
0.00145
1.00180
0.00131
1.00163
0.00119
0.85
1.00268
0.00137
1.00242
0.00124
1.00220
0.00112
1.00199
0.00103
I. OOI 80
0.00092
0.9
1.00286
0.00093
1.00260
0.00084
1.00234
0.00076
1. 002 1 2
0.00069
1. 00192
0.00062
0-9S
1.00298
0.00047
1.00269
0.00043
1.00243
0.00039
1.00220
0.00035
1.00200
0.00032
1.0
1. 0030 1
0.00
1.00273
0.00
1.00246
0.00
I.OO223
0.00
1.00202
0.00
1. 05
1.00298
0.00047
1.00269
0.00043
1.00243
0.00039
I.00220
0.00035
1.00200
0.00032
1.1
1.00286
0.00093
1.00260
0.00084
1.00234
0.00076
1. 002 1 2
0.00069
1.00192
0.00062
"S
1.00268
0.00137
1.00242
0.00124
1.00220
0.00112
I.OOI99
0.00103
1.00180
0.00092
1.2
1.00244
0.00177
1.00222
0.00160
1.00199
0.00145
I. OO 1 80
0.00131
1.00163
0.00119
1.25
1.00213
0.00213
1.00192
0.00193
1.00174
0.00174
I.OOI58
0.00158
1. 00143
0.00143
i-3
1.00177
0.00244
1. 00160
0.00220
1.00145
0.00199
I.OOI3I
0.00180
1.00118
0.00163
1 -35
1.00136
0.00268
1.00123
0.00243
1.00112
0.00220
I.OOIOI
0.00199
1. 0009 1
0.00180
1.4
1. 0009 1
0.00286
1 .00084
0.00259
1.00076
0.00234
I.OOO69
0.00212
1.00062
0.00192
1 -45
1.00047
0.00297
1.00042
0.00269
1.00038
0.00243
I.OOO35
0.00220
1. 0003 1
0.00200
i-5
1 .00000
0.00301
1 .00000
0.00272
1 .00000
0.00246
I. OOOOO
0.00223
I. OOOOO
0.00202
i-55
Q-99953
0.00297
0-99957
0.00269
0.99961
0.00243
0.99965
0.00220
0.99968
0.00200
1.6
0.99907
0.00286
0.99916
0.00259
0.99924
0.00234
O.9993I
0.00212
0.99938
0.00192
1.6s
0.99863
0.00268
0.99876
0.00242
0.99888
0.00219
O.99899
0.00198
0.99908
0.00179
i-7
0.99823
0.00243
0.99840
0.00220
0.99855
0.00199
O.99869
0.00180
0.99881
0.00163
1-75
0.99787
0.00212
0.90808
0.00192
0.99826
0.00174
O.99843
0.00157
0.99857
0.00142
1.8
o.99757
0.00176
0.99780
0.00160
0.99801
0.00144
O.9982O
0.00131
0.99837
0.00118
1.85
0.99732
0.00136
0.99758
0.00123
0.99781
0.00112
O.99802
0.00101
0.99821
0.00091
1.9
0.99715
0.00093
0.99742
0.00084
0.99766
0.00076
O.99788
0.00069
0.99809
0.00062
1 -95
0.99704
0.00047
0.99732
0.00042
o.99757
0.00038
O.99780
0.00035
0.99801
0.00031
2.0
0.99700
0.00
0.99728
0.00
o.99754
0.00
0.99777
0.00
0.99799
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (3.25 4- t o.75) = 1.00213 + * 0.00213.
tanh (3.30 + i 1 .50) = 1.00000 i 0.00272.
[87]
Table IX HYPERBOLIC TANGENTS, tanh (x + iq) = u + iv. Continued
x = 3-5o
x = 3-55
x = 3.60
x = 3-65
x = 3.70
0.99818
0.00
0-99835
0.00
0.99851
0.00
0.99865
0.00
0.99878
0.00
0.05
0.99820
0.00028
0.99837
0.00026
0.99853
0.00023
0.99867
0.00021
0.99879
0.00019
O.I
c.99827
0.00056
0.99843
0.00051
0.99858
0.00046
0.99872
0.00042
0.99884
0.00038
0.15
0.99837
0.00083
0.99853
0.00075
0.99867
0.00068
0.99880
0.00061
0.99891
0.00055
0.2
o-99853
0.00107
0.99867
0.00097
0.99879
0.00088
0.99891
0.00079
0.99901
0.00072
0.25
0.99871
0.00129
0.99883
0.00117
0.99894
0.00105
0.99904
0.00095
0.99914
0.00086
-3
0.99893
0.00147
0.99903
0.00133
0.99912
0.00121
0.99921
0.00109
0.99928
0.00099
o-35
0.99917.
0.00162
o.99925
0.00147
0.99932
0.00133
0.99939
0.00120
o.99944
0.00109
0.4
0.99944
0.00173
0.99949
0.00157
o.99954
0.00142
o.99958
0.00128
0.99962
0.00116
0-4S
0.99971
0.00180
0-99974
0.00163
o.99977
0.00147
0.99979
0.00133
0.99981
0.00121
-5
1. 00000
0.00182
1. 00000
0.00165
1. 00000
0.00149
1. 00000
0.00135
1. 00000
0.00122
0-5S
1 00028
0.00180
1.00026
0.00163
1.00025
0.00148
1. 0002 1
0.00133
1.00019
0.00121
0.6
1.00056
0.00174
1. 0005 1
0.00157
1.00048
0.00142
1.00042
0.00129
1.00038
0.00116
0.65
1.00083
0.00163
1.00075
0.00147
1.00068
0.00133
1. 0006 1
0.00120
1.00055
0.00109
0.7
1.00107
0.00148
1.00097
0.00134
1.00088
0.0012 1
1.00079
0.00109
1.00072
0.00099
0-7S
1.00129
0.00129
1. 001 1 7
0.00117
1. 00106
0.00106
1.00096
0.00096
1.00086
0.00086
0.8
1.00148
0.00107
1-00133
0.00097
1.00121
0.00088
1. 00108
0.00080
1.00099
0.00072
0.85
1.00163
0.00083
1.00147
0.00075
1.00133
0.00068
1.00120
0.00061
1. 00109
0.00056
0.9
1.00174
0.00056
1-00157
0.00051
1. 00142
0.00046
1. 00 1 29
0.00042
1.00116
00038
o-95
1. 00180
0.00029
1.00163
0.00026
1.00148
0.00023
1.00134
0.00021
1.00121
0.00019
1.0
1.00183
0.00
1.00165
0.00
1.00149
0.00
1.00135
0.00
1.00122
0.00
1. 05
1.00180
0.00029
1.00163
0.00026
1.00148
0.00023
1.00134
0.00021
1.00121
0.00019
1.1
1.00174
0.00056
1-00157
0.00051
1.00142
0.00046
1.00129
0.00042
1.00116
0.00038
i-i5
1.00163
0.00083
1.00147
0.00075
1.00133
0.00068
1.00120
0.00061
1.00109
0.00056
1.2
1.00148
0.00107
1. 00133
0.00097
1.00121
0.00088
1. 00108
0.00080
1.00099
0.00072
1.25
1.00129
0.00129
1.00117
0.00117
1.00106
0.00106
1 .00096
0.00096
1 .00086
0.00086
i-3
1.00107
0.00148
1.00097
0.00134
1.00088
0.00121
1.00079
0.00109
1.00072
0.00099
i-3S
1.00083
0.00163
1.00075
0.00147
1.00068
0.00133
1. 0006 1
0.00120
1.00055
0.00109
1.4
1.00056
0.00174
1. 0005 1
0.00157
1.00048
0.00142
1.00042
0.00129
1.00038
0.00116
i-45
1.00028
0.00180
1.00026
0.00163
1.00025
0.00148
1. 0002 1
0.00133
1. 00019
0.00121
i-5
1. 00000
0.00182
1. 00000
0.00165
1. 00000
0.00149
1. 00000
0.00135
1. 00000
0.00122
i-55
0.99971
0.00180
0-99974
0.00163
0-99977
0.00147
0.99979
0.00133
0.99981
0.00121
1.6
0.99944
0.00173
0.99949
0.00157
0.99954
0.00142
0.99958
0.00128
0.99962
0.00116
1.65
0.99917
0.00162
0.99925
0.00147
0.99932
0.00133
0-99939
0.00120
0.99944
0.00109
i-7
0.99893
0.00147
0-99903
0.00133
0.99912
0.00121
0.99921
0.00109
0.99928
0.00099
i-75
0.99871
0.00129
0.99883
0.00117
0.99894
0.00105
0.99904
0.00095
0.99914
0.00086
1.8
0.99853
0.00107
0.99867
0.00097
0.99879
0.00088
0.99891
6.00079
0.99901
0.00072
i.8s
0.99837
0.00083
0.99853
0.00075
0.99867
0.00068
0.99880
0.00061
0.99891
0.00055
1.9
0.99827
0.00056
0.99843
0.00051
0.99858
0.00046
0.99872
0.00042
0.99884
0.00038
i-95
0.99820
0.00028
0.99837
0.00026
0.99853
0.00023
0.99867
0.00021
0.99879
0.00019
2.0
0.99818
0.00
0.99835
0.00
0.99851
0.00
0.99865
0.00
0.99878
0.00
Note.
Negative quantities are in heavy type.
Examples, tanh (3.60 4-
i 0.80) =
1.00121 4-
i 0.00088
tanh (3.70 4- i 1.70) = 0.99928 i 0.00099.
[88]
Table IX. HYPERBOLIC TANGENTS, tanh (* + iq) =u+ iv. Continued
x = 3-75
x = 3.80
* = 3-85
x = 3.90
o
0.05
O.I
0.15
0.2
0.25
-3
o.35
0.4
0.45
0.5
o.55
0.6
0.65
0.7
o.75
0.8
0.85
0.9
o-95
1.0
1. 05
1.1
i-i5
1.2
1-25
i-3
i-35
1.4
i-45
i-S
i-55
1.6
1.6S
i-7
i-7S
1.8
1.85
1.9
1-95
0.99889
0.99891
0.99895
0.99901
0.9991 1
0.99922
o-9993S
0.99950
0.99966
0.99983
1. 00000
1.00017
1.00034
1.00050
1.00065
1.00078
1.00089
1.00099
1. 00 1 05
1. 00 109
I.OOIII
1. 00109
1.00105
1 .00099
1 .00089
1.00078
1.00065
1.00050
1.00034
1.00017
1. 00000
0.99983
0.99966
0.99950
99935
0.99922
0.999 1 1
0.99901
0.99895
0.99891
0.00
0.00017
0.00034
0.00050
0.00065
0.00078
0.00089
0.00099
0.00105
0.00109
O.OOIII
0.00109
0.00105
O.OOC99
0.00090
0.00078
0.00065
0.00050
0.00034
0.00017
0.00
0.00017
0.00034
0.00050
0.00065
0.00078
0.00090
0.00099
0.00105
0.00109
O.OOIII
0.00109
0.00105
0.00099
0.00089
0.00078
0.00065
0.00050
0.00034
0.00017
0.99900
0.99901
0.99905
0.9991 I
0.99919
0.99929
0.99941
o-99955
0.99969
0.99984
1. 00000
1.00016
1. 0003 1
1.00045
1.00059
1.0007 1
1. 0008 1
1.00089
1 .00096
1.00099
I.OOIOO
1.00099
1 .00096
1 .00089
1. 0008 1
1.00071
1.00059
1.00045
1.0003 1
1.00016
1. 00000
0.99984
0.99969
Q-99955
0.99941
0.99929
0.99919
0.999 1 1
0.99905
0.99901
0.00
0.00016
0.00031
0.00045
0.00059
0.00071
0.00081
0.00089
0.00095
0.00099
O.OOIOO
0.00099
0.00095
0.00089
0.00081
0.00071
0.00059
0.00045
0.00031
0.00016
0.00
0.00016
0.00031
0.00045
0.00059
0.00071
0.00081
0.00089
0.00095
0.00099
O.OOIOO
0.00099
0.00095
00089
0.00081
0.00071
0.00059
0.00045
0.00031
0.00016
0.99909
0.9991 1
0.99914
0.99919
0.99927
0.99936
0.99947
0.99959
0.99972
0.99986
1. 00000
1. 00014
1.00028
1. 0004 1
1.00053
1.00064
1.00073
1. 0008 1
1.00086
1.00089
1 .00090
1 .00089
1.00086
1. 0008 1
1.00073
1.00064
1.00053
I. 0004 I
1.00028
1.00014
1. 00000
0.99986
0.99972
0.99959
0.99947
0.99936
0.99927
0.99919
0.99914
0.999 1 1
0.00
0.00014
0.00028
0.00041
0.00053
0.00064
0.00073
0.00081
0.00086
0.00089
0.00091
0.00089
0.00086
0.00081
0.00073
0.00064
0.00053
0.00041
0.00028
0.00014
0.00
0.00014
0.00028
0.00041
0.00053
0.00064
0.00073
0.00081
0.00086
0.00089
0.00091
0.00089
0.00086
0.00081
0.00073
0.00064
0.00053
0.00041
0.00028
0.00014
2.0 0.99889 0.00
0.99900 0.00
0.99909 0.00
0.99918
0.99919
0.99922
0.99927
0.99934
0.99942
0.99952
0.99963
0.9997s
0.99987
1. 00000
1.00013
1.00025
1.00037
1 .00048
1.00058
1 .00066
1.00073
1.00078
1. 0008 1
1.00082
1. 0008 1
1.00078
1.00073
1.00066
1.00058
1 .00048
1.00037
1.00025
1.00013
I. 00000
0.99987
Q-99975
0.99963
0.99952
0.99942
0.99934
0.99927
0.99922
0.99919
0.99918 0.00
0.00
0.00013
0.00025
0.00037
0.00048
0.00058
0.00066
0.00073
0.00078
0.00081
0.00082
0.00081
0.00078
0.00073
0.00066
0.00058
0.00048
0.00037
0.00025
0.00013
0.00
0.00013
0.00025
0.00037
0.00048
0.00058
0.00066
0.00073
0.00078
0.00081
0.00082
0.00081
0.00078
0.00073
0.00066
0.00058
0.00048
0.00037
0.00025
0.00013
* = 3-95
0.99926 0.00
0.99927 0.00012
0.99930 0.00023
0.99934 0.00034
0.99940 0.00044
0.99948 0.00052
0.99956 0.00060
0.99966 0.00066
0.99977 0.00071
0.99988 0.00073
1. 00000 0.00074
1.00012 0.00073
1.00023 0.00071
1.00034 0.00066
1 .00044 0.00060
1.00052 0.00052
1 .00060 0.00044
1.00066 0.00034
1.00071 0.00023
1.00073 0.00012
1.00074 o-oo
1.00073 0.00012
1.00071 0.00023
1.00066 0.00034
1 .00060 0.00044
1.00052 0.00052
1.00044 0.00060
1.00034 0.00066
1.00023 0.00071
I. OOO 1 2 O.OOO73
I. OOOOO O.OOO74
O.99988 O.OOO73
O.99977 O.OOO71
O.99966 O.OO066
O.99956 O.OOO60
O.99948 O.OOO52
O.9994O O.OOO44
O.99934 O.OOO34
O.9993O O.OOO23
O.99927 O.OOOI2
O.99926 O.OO
Note. Negative quantities are in heavy type.
Examples, tanh (3.95 '+ i Q-95) = 1.00073 + i 0.00012.
tanh (3.95 + i 1.05) = 1.00073 i 0.00012.
[89]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r [y
x = 0.05
x m 0.15
0.05
0.1
0.15
0.2
0.25
-3
0.3s
0.4
0-4S
o-5
o-55
0.6
0.65
0.7
o.75
0.8
0.85
0.9
o-95
1.0
1.05
i.i
115
1.2
1-25
i-3
i-35
1.4
i-4S
i-5
i-55
1.6
1.6s
i-7
i-7S
1.8
1.8S
1.9
i-95
0.000 90
0.07846 90
0.15643 90
0.2334S 90
0.30902 90
0.38268 90
0-4S399 90
0.52250 90
0.58778 90
0.64944 90
0.70711 00
0.76041 90
0.80902 90
0.85264 90
0.89101 90
0.92388 90
0.95106 90
0.97237 90
0.98769 90
0.99692 90
1. 00000 90
0.99692 90
0.98769 90
0.97237 90
0.95106 90
0.92388 90
0.89101 90
0.85264 90
0.80902 90
0.76041 90
0.70711 90
0.64944 90
0.58778 90
0.52250 90
0-45399 90
0.38268 90
0.30902 90
0.23345 90
0.15643 90
0.07846 90
0.05002
0.09305
0.16424
0.23874
0.31304
0.38594
0.45672
0.52487
0.58989
0.65135
0.70803
0.76202
0.81053
0.85407
0.89237
0.92523
0.95237
0.97366
0.98895
0.99817
1.00125
0.99817
0.98895
0.97366
0.95237
0.92523
0.89237
0.85407
0.81053
0.76202
0.70803
0.65135
0.58989
0.52487
0.45672
0.38594
0.31304
0.23874
0.16424
0.09305
0.000
57-593
72.493
78.245
81.259
83-123
84.400
85-339
86.066
86.652
87.I39
87-557
87.921
88.246
88.542
88.814
89.070
89-313
89.547
89-775
90.000
90.225
90.453
90.687
90.930
91.186
91.458
91-754
92.079
92-443
92.860
93-348
93-934
94.661
95.600
96.877
98.741
101.755
107.507
122.407
0.10017
0.12724
0.18576
0.25403
0.32485
o.39558
0.46491
0.53201
0.59626
0.65713
0.71417
0.76698
0.81520
0.85851
0.89662
0.92930
0.95632
0.97752
0.99275
1. 00194
1 .00500
1. 00194
0.99275
o.97752
0.95632
0.92930
0.89662
0.85851
0.81520
0.76698
0.71417
0.65713
0.59626
0.53201
0.46491
o.39558
0.32485
0.25403
0.18576
0.12724
0.000
38.300
57-8i9
67-455
72.947
76.471
78.932
80.762
82.189
83-344
84.308
85-134
85.858
86.505
87.093
87.636
88.145
88.629
89.095
89-550
90.000
90.450
90.905
9i.37i
9I.855
92.364
92.907
93-495
94.142
94.866
95.692
96.656
97.811
99.238
101.068
103.529
107.053
112.545
122. 181
141.700
0.15056
0.16978
0.21712
0.27779
o.34375
0.41 1 24
0.47831
o.54376
0.60676
0.66667
0.72296
0.77527
0.82291
0.86583
0.90364
0.93607
0.96290
0.98396
0.99909
1.00822
1.01127
1.00822
0.99909
0.98396
0.96290
0.93607
0.90364
0.86583
0.82291
0.77527
0.72296
0.66667
0.60676
o.54376
0.47831
0.41 1 24
o.34375
0.27779
0.21712
0.16978
0.000
27.861
46.771
58.195
65.382
70.229
73-7"
76.344
78.419
80.1 1 1
81.532
82.753
83.826
84.787
85.662
86.471
87.231
87-953
88.649
89.329
90.000
90.671
9I-35I
92.047
92.769
93-529
94-338
95-213
96.174
97.247
98.468
99.889
101.581
103.656
106.289
109.771
114.618
121.805
133.229
152.139
0.20134
0.21608
0.25497
0.30827
0.36882
0.43422
0.49663
0-55995
0.62131
0.67994
0.73521
0.78661
0.83370
0.87609
0.91347
0.94556
0.97213
0.99300
1.00800
1. 01 704
1.02007
1. 01 704
1.00800
0.99300
0.97213
o.94556
0.91347
0.87609
0.83370
0.78661
0.73521
0.67994
0.62131
0-55995
0.49663
0.43242
0.36882
0.30827
0.25497
0.21608
0.000
21.739
38.746
50.576
S8.723
64.522
68.825
72.147
74.802
76.988
78.835
80.431
81.839
83-103
84-257
85.326
86.331
87.287
88.209
89.110
90.000
90.890
91.791
92.713
93.669
94.674
95-743
96.897
98.161
99.569
101.165
103.012
105.198
107.853
in. 175
115.478
121.277
129.424
141.254
158.261
2.0 0.00 90 0.05002 180.000 0.10017 180.000 0.15056 180.000 0.20134 180.000
Example. sinh (0.15 4- i 0.15) = 0.27779 /58.i95 = 0.27779 /58.ii , .42"
[90]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r /y. Continued
0.25
o-3
x = 0.35
x = 0.4
x = 0.45
0.25261
0.000
0.30452
0.000
o.357i9
0.000
0.41075
0.000
0.46534
0.000
0.05
0.26452
17.814
0.31447
15. 118
0.36571
13.169
0.41818
11.703
0.47191
10.567
O.I
0.29782
32.890
0.34235
28.533
0.38994
25.214
0-43953
22.629
0.49093
20.576
0.15
o-34396
44-943
0.38370
39-493
0.42671
35.5i6
0.47246
32.288
0.52062
29.642
0.2
o-399i3
52.992
0.43385
48.122
0.47231
44.008
0.51401
40.536
0.55860
37.601
0.25
0.45854
59.405
0.48906
54.882
0.52348
50.921
0.56140
47-471
0.60249
44-473
-3
o.5i9S4
64.327
0.54666
60.242
0.57766
56.843
0.61223
53.288
0.65012
50.374
o-3S
0.58036
68.215
0.60476
64-575
0.63292
61.237
0.66462
58.200
0.69968
55-454
0.4
0.63977
71-371
0.66199
68.151
0.68781
65-157
0.71708
62.393
0.74969
59-856
45
0.69685
73-999
0.71730
71.166
0.74119
68.503
0.76844
66.018
o.79895
63.712
o-5
0.75088
76.238
0.76989
73-759
0.79220
71.408
0.81775
69.196
0.84649
67.125
o-SS
0.80127
78.185
0.81912
76.028
0.84012
73-971
0.86426
72.021
0.89149
70.184
0.6
0.84754
79.911
0.86443
78.049
0.88436
76.267
0.90732
74.568
0-93330
72.958
0.65
0.88927
81.464
0.90539
79.878
0.92444
78.353
0.94642
76.893
0.97136
75-504
0.7
0.92612
82.887
0.94161
8i.557
0-95994
80.274
0.981 13
79-043
1.00521
77-868
o.75
o.95779
84.207
o.97277
83.119
0.99052
82.068
1.01107
81.056
1.03446
80.087
0.8
0.98403
85-450
0.99862
84-593
1-01592
83.762
I-03597
82.962
1.05880
82.194
0.85
1 .00464
86.635
1. 01 894
85.999
1.03590
85-383
1-05557
84.788
1.07798
84.216
0.9
1. 01949
87.779
I-03357
87-358
1.05029
86.951
1.06970
86.556
1.09182
86.177
o-95
1.02843
88.896
1.04239
88.687
1.05898
88.484
1.07822
88.287
1.10017
88.098
1.0
1.03141
90.000
1 -04534
90.000
1. 06 1 88
90.000
1. 08107
90.000
1. 10297
90.000
1.05
1.02843
91.104
1.04239
9I-3I3
1.05898
91.516
1.07822
9!-7i3
1.10017
91.902
1.1
1. 01 949
92.221
I-03357
92.642
1.05029
93-o5o
1.06970
93-444
1.09182
93-823
1.15
1.00464
93.365
1. 01 894
94.001
1.03590
94.617
I-05557
95-212
1.07798
95.784
1.2
0.98403
94-550
0.99862
95-407
1.01592
96.238
I-03597
97.038
1.05880
97.806
1 25
0.95779
95-793
0.97277
96.881
0.99052
97.932
1.01107
98.944
1.03446
99-9I3
i-3
0.92612
97-H3
0.94161
98.443
0-95994
99.726
0.981 13
100.957
1. 005 2 1
102.132
i-3S
0.88927
98.536
0.90539
100.122
0.92444
101.647
0.94642
103.107
0.97136
104.496
1.4
0.84754
100.090
0.86443
101.951
0.88436
103.733
0.90732
105.432
0.93330
107.042
i-45
0.80127
101.815
0.81912
103.972
0.84012
106.029
0.86426
107,979
0.89149
109.816
i-5
0.75088
103.762
0.76989
106.241
0.79220
108.592
0.81775
110.804
0.84649
112.875
i-5S
0.69685
106.001
0.71730
108.834
0.741 19
1 1 1. 497
0.76844
113.982
0.79S95
116.288
1.6
0.63977
108.629
0.66199
1 1 1. 849
0.68781
114.843
0.71708
117.607
0.74969
120.144
1.6S
0.58036
in. 785
0.60476
115-425
0.63292
118.763
0.66462
121.800
0.69968
124.546
i-7
o.5i954
"5- 6 73
0.54666
119.758
0.57766
123.157
0.61223
126.712
0.65012
129.626
1-75
0.45854
120.595
0.48906
125. 118
0.52348
129.079
0.56140
132.529
0.60249
I35-527
1.8
o.399i3
127.008
0.43385
131.878
0.47231
135-992
0.51401
139.464
0.55860
142.399
1.8s
o.34396
I35.057
0.38370
140.507
0.42671
144.484
0.47246
147.712
0.52062
150.358
1.9
0.29782
147. no
0.34235
151.467
0.38994
154.786
0-43953
157-371
0.49093
159.424
i-95
0.26452
162.186
0.31447
164.882
0.36571
166.831
0.41818
168.297
0.47191
I69-433
2.0 0.25261 180.000 0.30452 180.000 0.35719 180.000 0.41075 180.000 0.46534 180.000
Example. sinh (0.40 + i 0.25) = 0.56140 /47.47i = 0.56140 /47.28'.i6"
[91]
Table X.
HYPERBOLIC SINES.
sinh (x -f
iq) = r l
/y. Continued
* =
0.5
x =
o.55
x =
0.6
x =
0.65
x =
0.7
Q
r
y
r
y
r
y
r
y
r
7
o
0.52110
0.000
0.57815
0.000
0.63665
0.000
0.69675
0.000
0.75858
0.000
0.05
0.52697
9.665
0.58345
8.936
0.64147
8-337
0.70115
7-839
0.76263
7.419
0.1
0.54407
18.918
0.59894
17-559
0.65559
16.432
0.71409
15.486
0.77455
14.685
0.15
0.57100
27-453
0.62350
25-625
0.67810
24.086
0.73482
22.781
0.79369
21.665
0.2
0.60583
35-1"
0.65555
32.990
0.70769
3i-i74
0.76220
29.613
0.81911
28.263
0.25
0.64652
41.871
0.69333
39.610
0.74282
37.642
0.79492
35-926
0.84965
34.426
0.3
0.691 1 2
47-793
0.73510
45-5"
0.78194
43-494
0.83160
41.710
0.88406
40.I33
o-3S
0. 73 793
52.980
0.77927
50.759
0.82361
48.769
0.87090
46.989
0.92112
45-397
0.4
0.78552
57-542
0.82447
55-437
0.86650
53-529
0.91156
51-803
0.95966
50.245
o.45
0.83266
61.584
. 0.86951
59.628
0.90946
57.838
0.95249
56.204
0.99861
54-7i6
o-5
0.87837
65.198
0.91338
63.411
0.95149
61.762
0.99270
60.245
1.03704
58.853
0-5S
0.92182
68.462
0.95524
66.854
0.991 71
65.360
1-03134
63.976
1.07409
62.698
0.6
0.96232
71.441
0-99437
70.016
1.02948
68.685
1.06769
67-445
1. 1 0904
66.294
0.65
0.99927
74.189
1 .03004
72.948
1. 064 1 1
71.784
I.IOIII
70.694
1.14125
69.677
0.7
1.03220
76.751
1.06214
75-693
1.09509
74.696
1.13108
73.760
1.17019
72.884
o-7S
1.06070
79.164
1.08987
78.287
1. 12200
77-459
I-I57I5
76.678
i-i954i
75-946
0.8
1.08446
81.461
1.11300
80.763
1. 14448
80.102
1. 17892
79-477
1. 21653
78.890
0.85
1. 103 20
83.669
1.13127
83.148
1. 16226
82.653
1. 19623
82.185
1.23327
81.744
0.9
1.11672
85.814
1. 14446
85.467
1.17510
85.121
1. 20871
84.826
1-24538
84-532
o-95
1.1 2489
87.917
1. 15244
87.744
1. 18287
87.580
1. 21626
87.424
1. 25271
87.277
1.0
1. 12763
90.000
1.15510
90.000
1. 18547
90.000
1. 21879
90.000
1-25517
90.000
1. 05
1.1 2489
92.083
1. 15244
92.256
1. 18287
92.420
1. 21626
92.576
1. 25271
92.723
1.1
1.11672
94.186
1. 14446
94-533
1.17510
94.879
1. 20871
95-174
1.24538
95.468
i-i5
1. 103 20
96.331
1.13127
96.852
1. 16226
97-347
1. 19623
97-8i5
1.23327
98.256
1.2
1.08446
98-539
1.11300
99.237
1. 1 4448
99.898
1. 17892
100.523
1. 21653
IOI.IIO
1.25
1.06070
100.836
1.08987
101.713
1. 12200
102.541
I.I57I5
103.322
1.19541
104.054
i-3
1.03220
103.249
1.06214
104.307
1.09509
105.304
1.13108
106.240
1.17019
107. 116
1-35
0.99927
105. 811
1.03004
107.052
1. 0641 1
108.216
I.IOIII
109.306
1.14125
110.323
1.4
0.96232
108.559
0-99437
109.984
1.02948
iii-3I5
1.06769
112.555
1. 10904
113.706
1 -45
0.92182
m-538
0.95524
113.146
0.99174
114.640
1-03134
116.024
1.07409
117.302
i-5
0.87837
1 14.803
0.91338
116.589
0.95149
118.238
0.99270
H9-755
1.03704
121. 148
i-55
0.83266
118.416
0.86951
120.372
0.90946
122.162
0.95249
123.796
0.99861
125.284
1.6
0.78552
122.458
0.82447
124-563
0.86650
126.471
0.91156
128.197
0.95966
129-755
1.65
C73793
127.020
0.77927
129.241
0.82361
131. 231
0.87090
I33-OH
0.92112
134.603
i-7
0.691 1 2
132.207
0.73510
134.489
0.78194
136.506
0.83160
138.290
0.88406
139-867
i-75
0.64652
138.129
0.69333
140.390
0.74282
142.358
0.79492
144.074
0.84965
145-574
1.8
0.60583
144.889
0.65555
147.010
0.70769
148.826
0.76220
150.387
0.81911
I5I-737
1.85
0.57100
I52.547
0.62350
154-375
0.67810
I55.9I4
0.73482
157.219
0.79369
158.335
1.9
0.54407
161.082
0.59894
162.441
0.65559
163.568
0.71409
164.514
0-77455
165-315
i-95
0.52697
170.335
0.58345
171.064
0.64147
171.663
0.70115
172. 161
0.76263
172.581
2.0 0.52110 180.000 0.57815 180.000 0.63665 180.000 0.69675 180.000 0.75858 180.000
Example. sinh (0.70 + i 1.70) = 0.88406 /i39.867 = 0.88406 /i3o.52 / .oi"
[92]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r [y. Continued
x = 0.75
x = 0.85
x = 0.9
* - 0.95
0.00
0.0s
O.IO
0.15
0.2
0.25
o-3
o-35
0.4
o.45
o-5
0-5S
0.6
0.65
0.7
0-7S
0.8
0.85
0.9
o-95
1.0
1.05
1.1
1.2
1-25
i-3
i-3S
1.4
1 45
1-5
i-55
1.6
1.6s
i-7
i-7S
1.8
1.85
1.9
i-9S
0.82232
0.82605
0.83706
0.85481
0.87846
0.90700
0.93932
0.97427
1.01079
1.04785
1.08453
1.12001
I-IS356
1. 18457
1. 21248
1.23689
1.25726
1.27346
1.28520
1.29230
1.29468
1.29230
1.28520
1.27346
1.25726
1.23689
1. 21248
1. 18457
I-I5356
1.12001
1.08453
1.04785
1.01079
0.97427
0.93932
0.90700
0.87846
0.85481
0.83706
0.82605
0.000
7.064
14.002
20.706
27.093
33. in
38-737
43-974
48.840
53-363
57-578
61.522
65.228
68.733
72.067
75.260
78.339
81.330
84-2S5
87.138
90.000
92.862
95-745
98.670
101.661
104.740
107.933
in. 267
114.772
118.478
122.422
126.637
131. 160
136.026
141.263
146.889
152.907
159.294
165.998
172.936
0.8881 1
0.89157
0.90178
0.91828
0-94033
0.96705
0.99742
1. 0304 1
1.06500
1. 10024
1.13522
1.16917
1. 20135
1-23115
1.25802
1. 28152
1-30124
1.31691
1.32825
I-335I3
1-33743
I-335I3
1.32825
1.31691
1-30124
1. 28152
1.25802
1.23115
1. 20135
1.16917
1. 13522
1. 10024
1.06500
1. 0304 1
0.99742
0.96705
0.94033
0.91828
0.90178
0.89157
0.000
6-759
13.415
19.877
26.073
3 I -955
37-500
42.702
47-574
52.135
56.414
60.441
64.245
67.857
71.307
74.621
77.825
80.942
83.996
87.008
90.000
92.992
96.004
99.058
102.175
105-379
108.693
112. 143
"5-755
"9-559
123.586
127.865
132.426
137.298
142.500
148.045
153.927
160.123
166.585
173.241
2.0 0.82232 180.000 0.8881 1 180.000
0.95612
0-95933
0.96883
0.98420
1. 0048 1
.02985
05843
08957
.12234
15583
.18918
.22163
.25246
.28107
30693
32955
34858
36369
37466
.38130
38353
.38130
37466
.36369
.34858
32955
.30693
.28107
.25246
.22163
15583
.12234
08957
05843
02985
.00481
0.98420
0.96883
0-95933
0.95612
0.000
6.497
12.909
19.158
25.181
30.938
36.401
41-565
46.433
51.022
55-353
59-450
63-399
67.048
70.602
74.026
77-344
80.580
83-754
86.887
90.000
93-113
96.246
99.420
102.656
105.974
109.398
112.952
116.601
120.550
124.647
128.978
I33-567
I38-435
143-599
149.062
154.819
160.842
167.091
I73.503
.02652
.02951
03837
05273
.07202
09553
.12243
.15184
.18289
.21471
.24649
.27748
.30700
33444
35927
.38105
39937
41395
.42452
.43094
43309
43094
42452
41395
39937
.38105
35927
33444
.30700
.27748
.24649
.21471
.18289
.15184
.12243
09553
.07202
05273
03837
.02951
0.000
6.270
12.468
18.529
24.399
30.039
35426
40.547
45-407
50.014
54-386
58.543
62.507
66.301
69.949
73474
76.898
80.242
83-527
86.773
90.000
93.227
96473
99-758
103.102
106.526
1 10.051
113.699
"7493
121.457
125.614
129.986
134-593
139453
144-574
149.961
155.601
161.471
167-532
I73.730
1.09948
1. 10227
1.11056
1. 12400
1. 14209
1.16418
1. 19227
1. 21732
1.24674
1.27697
1.30723
1.33682
1-36505
1-39136
1.41519
1. 436 1 1
I4537I
1.46778
1.47797
1. 4841 5
1.48623
1.48415
1.47797
1.46778
I4537I
1. 436 1 1
1.41519
1.39136
1-36505
1.33682
1.30723
1.27697
1.24674
1. 21732
1 19227
1.16418
1. 14209
1. 12400
1.11056
1. 10227
0.000
6.073
12.085
17.980
23.712
29.245
34-557
39-637
44.483
49.102
53-507
57-714
6i.743
65.613
69-347
72.963
76.484
79.929
83-316
86.668
90.000
93-332
96.684
100.071
103.516
107.037
110.653
114.387
118.257
122.286
126.493
130.898
I35-5I7
140.363
145-443
150.755
156.288
162.020
167.915
173.927
180.000 1.02652 180.000 1.09948 180.000
Example. sinh (0.90 + iLi.o) = 1.43309 /90 .
[93]
Table X. HYPERBOLIC SINES, sinh (x +
iq) = r l_
'7. Continued
x =
1.0
x =
1.05
x -
= 1.1
x =
1.15
x =
1.2
1
r
y
r
y
r
y
r
y
r
y
o
1.17520
0.000
1.25386
0.000
I-33565
0.000
1.42078
0.000
1.50946
0.000
0.05
1. 17782
5.900
1. 25631
5-748
1-33795
5-615
1.42294
5497
1.51150
5-393
O.I
1. 18552
n.748
1.26358
"453
1.34478
11. 192
1.42936
10.961
I.5I755
io.757
0.15
1.19816
17.496
1.27540
17.071
1-3559
16.694
1-43983
16.361
1-52741
16.065
0.2
1.21515
23-105
1. 29137
22.568
I-37093
22.092
1-45399
21.670
I-54077
21.294
0.25
1-23594
28.541
i-3io95
27-9*5
I-38939
27-359
1.47141
26.864
I-5572I
26.421
-3
1.25984
33-784
1-3335*
33-093
1.41070
32.477
I-49I55
31.926
1.57626
31-433
o-35
1. 28612
38.821
I-35837
38.090
I-4342I
37-435
1.51381
36.847
1-59733
36-319
0.4
1. 3 1400
43-651
1.38479
42.902
1.45926
42.227
1-53756
41.620
1.61987
4i-o73
0-4S
1.34272
48.276
1.41207
47-530
1. 485 1 7
46.855
1.56217
46.245
1.64325
45-693
0-5
I-37IS3
52.707
i-4395o
51.981
1.51128
51-323
1-58701
50.725
1.66688
50.184
o-55
1.39976
56-957
1. 46641
56.268
I.53694
55-640
1.61147
55-069
1. 690 1 8
54-549
0.6
1.42675
61.043
1.49220
60.403
1-56156
59-8i8
1.63497
59.284
1. 71260
58.797
0.65
M5*93
64.981
1-51630
64.401
1.58460
63.870
1.65699
63-384
I-73363
62.939
0.7
1.47479
68.791
1.53820
68.280
1.60558
67.811
1.67705
67.380
1.75282
66.986
0-7S
1.49487
72.491
1-55747
72.056
1.62404
71.656
1.69472
71.287
1.76975
70.950
0.8
1.51182
76.101
1-57374
75-747
1.63965
75-421
1. 70971
75.120
1.78409
74.844
0.85
1-52532
79.638
1.58671
79.369
1.65211
79.121
1. 72166
78.893
1-79555
78.682
0.9
I-535I3
83.122
1. 59614
82.941
1.66117
82.774
1.73036
82.620
1.80389
82.478
o-95
1. 54108
86.724
1.60187
86.479
1.66667
86-395
I-73564
86.317
1.80895
86.246
1.0
1.54308
90.000
1.60379
90.000
1.66852
90.000
1-7374*
90.000
1.81066
90.000
1.05
1.54108
93.276
1.60187
93-521
1.66667
93-605
I-73564
93-683
1.80895
93-754
1.1
I-535I3
96.878
1-59614
97-059
1.66117
97.226
1.73036
97.380
1.80389
97.522
i.*l
1-52532
100.362
1-58671
100.631
1.65211
100.879
1. 72166
101.107
1-79555
101.318
1.2
1.51182
103.899
1-57374
104.253
1.63965
104.579
1. 70971
104.880
1.78409
105.156
1.25
1.49487
107.509
1-55747
107.944
1.62404
108.344
1.69472
108.713
1.76975
109.050
i-3
1.47479
in. 209
1.53820
in. 720
1.60558
112. 189
1.67705
112.620
1.75282
113-014
i-35
i-45 193
115.019
1.51630
"5-599
1.58460
116. 130
1.65699
116.616
I-73363
1 1 7.061
1.4
1.42675
118.957
1.49220
H9-597
1-56156
120.182
1.63497
120.716
1. 71260
121.203
i-45
1.39976
123.043
1. 4664 1
123.732
I.53694
124.360
1.61147
124.931
1. 69018
125451
i-5
I-37I53
127.293
i-4395o
128.019
1.51128
128.677
1-58701
129.275
1.66688
129.816
i-55
1.34272
131.724
1. 41 207
132.470
1. 485 1 7
i33- I 45
1-56217
133-755
1-64325
I34-307
1.6
1. 3 1400
136-349
1.38479
137.098
1.45926
137-773
1-53756
138.380
1.61987
138.927
1.65
1. 28612
141-179
I-35837
141.910
1.43421
142-565
1.51381
143-153
1-59733
143.681
i-7
1.25984
146.216
I-3335I
146.907
1.41070
147-523
I-49I55
148.074
1.57626
148.567
i-7S
1-23594
i5!-459
i-3 IQ 95
152.085
1.38939
152.641
I-47I4I
I53-I36
I-5572I
153-579
1.8
1-21515
156.895
1. 29137
157432
1-37093
157.908
1-45399
158.330
I-54077
158.706
1.8S
1.19816
162.504
1.27540
162.929
I-35590
163.306
I-43983
163.639
I-5274I
163.935
1.9
1. 18552
168.252
1.26358
168.547
1.34478
168.808
1.42936
169.039
I-5I755
169.243
i-9S
1. 17782
174.100
1.25631
174.252
1-33795
174-385
1.42294
174-503
1-51150
174.607
2.00 1. 17520 180.000 1.25386 180.000 1.33565 180.000 1.42078 180.000 1.50946 180.000
Example. sinh (1.20 4- i 1.25) = '1.76975 /io9.o5o = 1.76995 / iocf .0$' .00"
[94]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r Ay. Continued
x = 1.25
x = 1.3
* = 1-35
x = 1.4
* = 1 -45
1.60192
0.000
1.69838
0.000
1.79909
0.000
1.90430
0.000
2.01427
0.000
0.05
1.60384
5-3QI
1. 70019
5.218
1.80080
5-145
1.90592
5.080
2.01580
5.021
O.I
1.60954
10.576
I-70557
10.415
1.80588
10.271
1.91072
10.143
2.02034
10.028
0.15
1.61884
15-803
I-7I435
I5-568
1.81417
15-359
1.91856
15.172
2.02775
15-005
0.2
1-63145
20.958
1.72627
20.659
1.82544
20.392
1.92921
20.153
2.03784
19-939
0.25
1.64699
26.026
1.74096
25-673
I-83934
25-356
1.94237
25-073
2.05030
24.818
-3
1.66501
30.991
1.75802
30-595
1-85549
30.240
1.95767
29.921
2.06479
29.634
o-35
1.68497
35-845
1.77694
35-4i8
1-87343
35-035
1.97468
34.689
2.08093
34-379
0.4
1.70635
40.580
1.79722
40.135
1.89268
39-735
1.99295
39-373
2.09828
39047
0-4S
1.72856
45-195
1.81832
44-745
1.91273
44-338
2.01200
43-970
2.11637
43-638
o-5
1. 75 104
49.693
1.83970
49.248
1.93306
48.845
2.03135
48.480
2.13478
48.150
o-55
I-77323
54-Q77
1.86084
53-648
I-953I9
53-258
2.05051
52-905
2.15302
52.584
0.6
1.79462
58.354
1.88123
57-95Q
1.97262
57-583
2.06903
57-249
2.17067
56.945
0.65
1. 81470
62.533
1 .90040
62.163
1. 9909 1
61.825
2.08647
61.518
2.18731
61.238
0.7
1.83304
66.625
1.91792
66.295
2.00764
65.994
2.10244
65-7I9
2.20254
65.469
0-7S
1.84924
70.640
I-9334I
70.356
2.02245
70.097
2.11658
69.861
2.21604
69.645
0.8
1.86297
74-590
1.94654
74-358
2.03500
74-145
2.12858
73-951
2.22751
73-774
0.85
1.87394
78.489
1.95704
78.311
2.04505
78.149
2.13819
78.000
2.23669
77.864
0.9
1.88193
82.348
1.96470
82.228
2.05238
82.118
2.14520
82.018
2-24334
81.925
0-9S
1.88679
86.180
I-96935
86.120
2.05684
86.065
2.14947
86.014
2.24747
85.968
1.0
1.88842
90.000
1.97091
90.000
2.05833
90.000
2.15090
90.000
2.24884
90.000
1.05
1.88679
93.820
I-96935
93.880
2.05684
93-935
2.14947
93.986
2.24747
94.032
1.1
1.88193
97.652
1.96470
97.772
2.05238
97.882
2.14520
97.982
2-24334
98.075
i-i5
1.87394
101.511
1.95704
101.689
2.04505
101.851
2.13819
102.000
2.23669
102.136
1.2
1.86297
105.410
1.94654
105.642
2.03500
105-855
2.12858
106.049
2.22751
106.226
1-25
1.84924
109.360
I-9334I
109.644
2.02245
109.903
2.11658
110.139
2.21604
no-355
i-3
1.83304
H3-375
1.91792
113-705
2.00764
114.006
2.10244
114. 281
2.20254
ii4-53i
1-35
1.81470
117.467
1.90040
117-837
1. 9909 1
118.175
2.08647
118.482
2.18731
118.762
1.4
1.79462
121 .646
1.88123
122.050
1.97262
122.417
2.06903
122.751
2.17067
123.055
1 -45
I-77323
125.923
1.86084
126.352
I-953I9
126.742
2.05051
127.095
2.15302
127.416
x-5
1. 75104
130.308
1.83970
130.752
1.93306
I3i-i55
2:03135
131.520
2.13478
131-851
i-5S
1.72856
134.805
1.81832
135-255
1.91273
135.662
2.01200
136.030
2.11637
136.362
1.6
1.70635
139.420
1.79722
139.865
1.89268
140.265
1.99295
140.627
2.09828
140.953
1.6S
1.68497
I44-I55
1.77694
144.582
1-87343
144.965
1.97468
i45-3ii
2.08093
145.621
i-7
1.66501
149.009
1.75802
149.405
1-85549
149.760
1.95767
150.079
2.06479
150.366
i-7S
1.64699
153-974
1.74096
I54-327
1-83934
154.644
1.94237
I54-927
2.05030
155.182
1.8
1-63145
159.042
1.72627
I59-34I
1.82544
159.608
1.92921
159.847
2.03784
160.061
1-85
1. 6 1 884
164.197
I-7I435
164.432
1.81417
164.641
1.91856
164.828
2.02775
164.995
1.9
1.60954
169.424
I-70557
169.585
1.80588
169.729
1.91072
169.857
2.02034
169.972
1-95
1.60384
174.699
1. 70019
174.782
1.80080
I74-855
1.90592
174.920
2.01580
174.979
2.0 1.60192 180.000 1.69838 180.000 1.79909 180.000 1.90430 180.000 2.01427 180.000
Example. sinh (1.45 + i 1.70) = 2.06479 / I 5Q-366 = 2.06479 /i5Q-22 / .oi"
[95]
Table X. HYPERBOLIC SINES, sinh (* + iq) = r fa. Continued
* = 1.50
x = 1.55
x = 1.60
* = 1.65
x = 1.70
2.12928
0.000
2.24961
0.000
2-37557
0.000
2.50746
0.000
2.64563
0.000
0.0s
2.13073
4.969
2.25098
4-923
2.37686
4.881
2.50869
4-843
2.64679
4.809
O.I
2.13502
9-925
2.25504
9-833
2.38071
9-751
2.5 J 234
9.677
2.65025
9.610
0.15
2.14204
14-855
2.26169
14.721
2.38701
14.600
2.51831
14.492
2-65591
14-395
0.2
2.ISIS9
19.746
2.27074
19-574
2-39558
19.419
2.52644
19.280
2.66361
i^SS
0.25
2.16340
24.590
2.28193
24-385
2.40619
24.200
2.53650
24.034
2.67316
23.884
o-3
2.17714
29.376
2.29496
29.144
2.41856
28.935
2.54824
28.747
2.68430
28.578
o-35
2.19245
34.099
2.30949
33-846
2.43235
33-6i9
2.56133
33415
2.69673
33.229
0.4
2.20892
38.753
2.32513
38.488
2.44721
38-248
2.57544
38.032
2.71014
37.837
o-4S
2.22612
43-337
2.34148
43.066
2.46274
42.820
2.59021
42.599
2.72418
42.398
0.5
2.24362
47.850
2.35812
47.580
2.47857
47-334
2.60527
47.113
2.73850
46.911
-55
2.26098
52.294
2-37465
52.030
2.49430
5I-79I
2.62024
51.574
2.75274
51-378
0.6
2.27779
56.670
2.39066
56.420
2-50955
56.192
2.63476
55.986
2.76657
55-799
0.65
2.29365
60.984
2.40577
60.752
2.52395
60.542
2.64847
60.351
2.77963
60.178
0.7
2.30819
65.241
2.41976
65-033
2.53717
64.845
2.66108
64.673
2.79164
64-5I7
o.75
2.32107
69.448
2. 43 1 93
69.268
2.54890
69.105
2.67226
68.956
2.80230
68.821
0.8
2.33202
73.611
2.44238
73464
2.55887
73.329
2.68178
73.206
2.81138
73-094
0.85
2.34080
77.740
2.45076
77.626
2.56687
77.523
2.68941
77.429
2.81867
77-343
0.9
2.34720
81.842
2.45688
81.765
2.57272
81.695
2.69499
81.631
2.82399
8i-573
o-95
2.35110
85-925
2.46061
85.887
2.57627
85.851
2.69839
85.819
2.82723
85.790
1.0
2-35241
90.000
2.46186
90.000
2.57746
90.000
2.69951
90.000
2.82832
90.000
1.05
2.35110
94-075
2.46061
94-H3
2.57627
94.149
2.69839
94.181
2.82723
94.210
1.1
2.34720
98.158
2.45688
98-235
2.57272
98-305
2.69499
98.369
2.82399
98.427
SM5
2.34080
102.260
2.45076
102.374
2.56687
102.477
2.68941
102.571
2.81867
102.657
1.2
2.33202
106.389
2.44238
106.536
2.55887
106.671
2.68178
106.794
2.81 138
106.906
1.25
2.32107
110.552
2 -43 1 93
110.732
2.54890
110.895
2.67226
III .044
2.80230
in. 179
i-3
2.30819
H4-759
2.41976
114.967
2.53717
II5.I55
2.66108
115.327
2.79164
1 1 5483
i-3S
2.29365
119.016
2.40577
119.248
2-52395
119.458
2.64847
119.649
2.77963
119.822
1.4
2.27779
123.330
2.39066
123.580
2-50955
123.808
2.63476
124.014
2.76657
124.201
1. 45
2.26098
127.706
2.37465
127.970
2.49430
128.209
2.62024
128.426
2.75274
128.622
i-5
2.24362
132.150
2.35812
132.421
2.47857
132.666
2.60527
132.887
2.73850
133.089
i-55
2.22612
136.663
2.34148
136.934
2.46274
137.180
2.59021
137.401
2.72418
137.602
1.6
2.20892
141.247
2.32513
141. 512
2.44721
I4L752
2.57544
141.968
2.71014
142.163
1.6s
2.19245
145.901
2.30949
146.154
2.43235
146.381
2.56133
146.585
2.69673
146.771
i-7
2.17714
150.624
2.29496
150.856
2.41856
151.065
2.54824
151.253
2.68430
151.422
i-75
2.16340
i55.4io
2.28193
I55-6I5
2.40619
155.800
2.53650
155.966
2.67316
156. 116
1.8
2.15159
160.254
2.27074
160.426
2-39558
160.581
2.52644
160.720
2.66361
160.845
1.85
2.14204
165-145
2.26169
165.279
2.38701
165.400
2.51831
165.508
2.65591
165.605
1.9
2.13502
170.075
2.25504
170.167
2.38071
170.249
2-51234
170.323
2.65025
170.390
1 -95
2.13073
175-031
2.25098
175.077
2.37686
I75.II9
2.50869
175-157
2.64679
I75-I9I
2.0 2.12928 180.000 2.24961 180.000 2.37557 180.000 2.50746 180.000 2.64563 180.000
Example. sinh (1.55 + i 0.60) = 2.39066 /56.42o = 2.39066 /56 . 25^.1 2*
[96]
Table X. HYPERBOLIC SINES, sinh (* + iq) = r
Continued
x = 1-75
x = 1.85
x = 1.9
x = 1.95
2.79041
0.00
2.94217
0.00
3.10129
0.00
3.26816
0.00
344321
0.00
0.05
2.79151
4-779
2.94322
4-752
3.10228
4.727
3.26911
4-705
3.44410
4.685
O.I
2.79479
9-551
2-94633
9-497
3- io 523
9.448
3.27191
9405
344675
9-365
0.15
2.80016
14-307
2.95142
14.228
3.1 1006
14.158
3.27649
14.094
345"2
14.036
0.2
2.80747
19.042
2-95835
18.941
3-11665
18.850
3.28274
18.767
345702
18.693
0.25
2.81653
23-75
2.96695
23.629
3-12481
23.520
3.29049
23.421
3.46441
23-332
o-3
2.82710
28.425
2.97699
28.287
3-J3434
28.163
3-29955
28.051
3473oi
27.950
o-3S
2.83891
33-063
2.98821
32.912
3.14500
32.776
3.30967
32-654
3.48263
32.543
0.4
2.85165
37.661
3.00031
37-5QI
3-15650
37-357
3.32060
37.227
349302
37.110
0-4S
2.86499
42.216
3.01300
42-053
3.16856
41.904
3-33207
41.770
3.50393
41.649
o-5
2.87861
46.730
3-02595
46.565
3.18088
46.416
3-34378
46.281
3-51507
46.160
o-55
2.89217
51.200
3-03885
51-039
3- I 93i5
50.893
3-35546
50.761
3.52617
50.642
0.6
2.90532
55-630
3-05138
55-476
3.20507
55-337
3.36681
55-2H
3-53698
55-096
0.65
2.91777
60.020
3-06323
59-877
3.21636
59.748
3.37756
59-631
3-54721
59.524
0.7
2.92921
64-375
3-07413
64.246
3.22675
64.129
3-38745
64.023
3-55663
63.927
o-75
2-93938
68.698
3.08382
68.586
3.23598
68.484
3-39624
68.392
3-56500
68.308
0.8
2.94804
72.992
3.09206
72.900
3-24384
72.816
3-40373
72.740
3.572I3
72.670
0.85
2.95498
77.265
3.09869
77-194
3.25015
77.129
340975
77.071
3-57788
77.017
0.9
2.96006
81.520
3-10353
81.471
3-25477
81.428
34I4I5
81.388
3.58207
81.352
0-9S
2.96315
85-763
3.10648
85.738
3-25759
85.716
3.41683
85.696
3.58462
85.678
1.0
2.96419
90.000
3.10747
90.000
3-25853
90.000
341773
90.000
3-58548
90.000
1. 05
2.96315
94-237
3.10648
94.262
3-25759
94.284
3.41683
94.304
3.58462
94.322
1.1
2.96006
98.480
3-10353
98.529
3-25477
98-572
34I4I5
98.612
3.58207
98.648
i-i5
2.95498
102.735
3.09869
102.806
3-25015
102.871
340975
102.929
3-57788
102.983
1.2
2.94804
107.008
3.09206
107.100
3-24384
107.184
340373
107.260
3.57213
107.330
1.25
2-93938
1 1 1.302
3-08382
in. 414
3.23598
111.516
3-39624
1 1 1.608
3-56500
in. 692
i-3
2.92921
115.625
3-o74i3
"5-754
3.22675
115-871
3-38745
H5-977
3-55663
116.073
1 -35
2.91777
119.980
3.06323
120.123
3.21636
120.252
3.37756
120.369
3-54721
120.476
1.4
2.90532
124.370
3-05138
124.524
3.20507
124.663
3.36681
124.789
3-53698
124.904
i-45
2.89217
128.800
3-03885
128.961
3.I93I5
129.107
3^5546
129.239
3.52617
129.358
i-5
2.87861
133.270
3-02595
133-435
3.18088
133-584
3-34378
I33-7I9
3-51507
133.840
i-55
2.86499
I37-784
3.01300
137-947
3.16856
138.096
3-33207
138.230
3.50393
138.351
1.6
2.85165
I42-339
3.00031
142.499
3- ^650
142.643
3.32060
142.773
349302
142.890
1.65
2.83891
146.937
2.98821
147.088
3.14500
147.224
3.30967
147.346
3.48263
147457
i-7
2.82710
151-575
2.97699
I5I-7I3
3- J 3434
151-837
3-29955
151.949
347301
152.050
i-75
2.81653
156.250
2.96695
156.371
3.12481
156.480
3.29049
I56.579
3.46441
156.668
1.8
2.80747
160.958
2-95835
161.059
3.11665
161. 150
3.28274
161.233
345702
161.307
1.85
2.80016
165.693
2.95142
165.772
3.11006
165.842
3.27649
165.906
345 112
165.964
1.9
2.79479
170.449
2.94633
170.503
3-10523
170.552
3.27191
170.595
3.4467S
170.635
1-95
2.79151
175.221
2.94322
175.248
3.10228
I75.273
3.26911
I75.295
3.44410
I75.3I5
2.0
2.79041
180.000
Example
2.94217
sinh (
180.000 3.10129 180.000
1.90 + i 2.0) = 3.26816 /180
3.26816
= 3.268
180.000
3-44321
180.000
16 \i8o.o
[97]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r /y. Continued
x =
2.0
x =
2.05
x =
2.1
x =
2.15
x =
2.2
?
r
7
r
7
r
7
r
7
r
7
o
3.62686
0.000
2.81950
0.000
4.02186
0.000
4.23419
0.000
4-457"
0.000
0.05
3.62771
4.667
3.82039
4.651
4.02263
4.636
4.23491
4.623
4-45779
4.6 1 1
O.I
3.63023
9-330
3.82279
9.298
4.02490
9.269
4.23707
9-243
4-4598S
9.220
0.15
3-63437
13.984
3.82671
I3-938
4.02863
I3-895
4.24061
I3.857
4.46322
13-823
0.2
3.64000
18.626
3.83206
18.566
4-0337I
18.511
4-24544
18.462
4.46780
18.418
0.2s
3.64699
23.252
3.83870
23.180
4.04002
23.114
4-25145
23-055
4-47350
23.002
o-3
3-65SI7
27-858
3.84648
27.776
4.04740
27.701
4.25846
27.634
4.48017
27-573
o-35
3.66430
32-443
3-85515
32-353
4.05566
32.271
4.26630
32.197
4.48763
32.130
0.4
3.67418
37.004
3-86454
36.908
4.06459
36.821
4.27479
36.743
4-49570
36.671
0-4S
3-68455
41-539
3.87440
41.440
4.07396
4I.35I
4.28371
41.270
4.50417
41.196
0.5
3-695I5
46.049
3.88448
45-950
4-08355
45.859
4.29282
45.778
4-51285
45-703
0-5S
3-70572
50.533
3-89453
50-435
4.093 1 1
50.347
4-30193
50.266
4-52i5o
5o-i93
0.6
2.71600
54.992
3-90432
54-898
4.10243
54.8I3
4.31079
54.736
4-52993
54.666
0.65
3-72574
59-427
3-9!359
59-340
4.11125
59.260
4.31918
59.188
4-53793
59-123
0.7
3-73470
63.840
3.92213
63.761
4-11938
63.689
4-32693
63.624
4-54529
63-565
0-7S
3.74268
68.232
3.92972
68.164
4.12661
68.101
4-3338i
68.044
4-55i84
67.993
0.8
3-74948
72.608
3.93620
72-551
4.13278
72.499
4-33968
72.452
4-55744
72.409
0.85
3-75495
76.969
3.94142
76.925
4-13774
76.885
4.34440
76.849
4.56167
76.816
0.9
3-75894
81.319
3-94521
81.289
4-14136
81.262
4-34785
81.237
4-56523
81.215
0-9S
3-76i37
85.661
3-94753
85.646
4-14357
85.632
4.34996
85.620
4-56723
85.609
1.0
3.76220
90.000
3-94832
90.000
4-I443I
90.000
4-35067
90.000
4.56791
90.000
1. 05
3-76i37
94-339
3-94753
94-354
4-14357
94.368
4.34996
94.380
4-56723
94-391
1.1
3-75894
98.681
3-94521
98.711
4.14136
98.738
4-3478S
98.763
4-56523
98.785
i-i5
3-75495
103.031
3.94142
103-075
4-13774
103. 115
4.34440
103. 151
4.56167
103.184
1.2
3-74948
107.392
3.93620
107.449
4.13278
107.501
4-33968
107.548
4-55744
107.591
1-25
3.74268
in. 768
3.92972
111.836
4.12661
I 1 1. 899
4-3338i
1 1 1. 956
4-55i84
112.007
i-3
3-7347Q
116. 160
3.92213
116.239
4.11938
116.311
4-32693
116.376
4-54529
116.435
i-35
3-72574
120.573
3-9I359
120.660
4.11125
120.740
4.31918
120.812
4-53793
120.877
1.4
3.71600
125.008
3-90432
125.102
4.10243
125.187
4.31079
125.264
4-52993
125.334
1-45
3-70572
129.467
3-89453
129.565
4.093 1 1
129.653
4-3 OI 93
129.734
4.52150
129.807
i-5
3-695I5
133-951
3.88448
134-051
4-08355
134.141
4.29282
134.223
4-51285
I34.297
i-55
3-68455
138.461
3.87440
138.560
4.07396
138.649
4.28371
138.730
4.50417
138.804
1.6
3.67418
142.996
3-86454
143.092
4.06459
i43- J 79
4.27479
I43.257
4-495 70
143-329
1.6S
3.66430
147-557
3-855I5
147.647
4.05566
147.729
4.26630
147.803
4.48763
147.870
i-7
3-655I7
152.142
3.84648
152.224
4.04740
152.299
4.25846
152.366
4.48017
152.427
i-75
3.64699
156.748
3.83870
156.820
4.04002
156.886
4-25I45
156.945
4-47350
156.998
1.8
3.64000
161.374
3.83206
161.434
4-0337I
161.489
4-24544
161.538
4.46780
161.582
1.85
3-63437
166.016
3.82671
166.062
4.02863
166.105
4.24061
166.143
4.46322
166.177
1.9
3-63023
170.670
3.82279
170.702
4.02490
170.731
4.23707
170.757
445985
170.780
1 -95
3.62771
175-333
3.82039
175-349
4.02263
175-364
4.23491
175-377
4-45779
I75.389
2.0 3.62686 180.000 3.81958 180.000 4.02186 180.000 4.23419 180.000 4.4571 1 180.000
Example. sinh (2.0 + i 1.0) = 3.76220 /go
[98]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r /y. Continued
* = 2.25
x = 2.3
* - 2.35
x = 2.4
x = 2.45
4.691 1 7
0.000
4.93696
0.000
5-I95IO
0.000
5.46623
0.000
5-75I03
0.000
0.05
4.69182
4.601
4-93759
4-591
5-I9569
4.582
5.46679
4-574
5.75I56
4-567
O.I
4-69377
9.199
4-93944
9.180
5-19745
9.163
5.46847
9.147
5.753I6
9-133
0.15
4.69697
13.792
4.94249
13-764
5-20035
13-739
5.47122
13.716
5-75576
I3-695
0.2
4.70134
18.378
4.94662
18.341
5.20428
18.309
547495
18.279
5-75932
18.252
0.25
4.70675
22.954
4-95177
22.910
5.20917
22.871
5.47961
22.835
5-76375
22.803
o-3
4.71308
27.518
4.95780
27.469
5.21490
27.424
548505
27-383
5.76892
27-347
o-3S
4.72017
32.070
4.96454
32.016
5-22131
31.966
549II5
31.922
5-77472
31.881
0.4
4.72784
36.608
4.97183
36-549
5.22825
36497
549775
36.449
5.78099
36.407
0-4S
4-73592
41.130
4-97950
41.070
5-23553
41.016
5.50468
40.966
5.78758
40.922
S
4-744IS
45-636
4-98734
45-576
5.23728
45-521
5-5II77
45471
5-79434
45427
o-55
4.75240
50.127
4.99518
50.068
5.25046
50.014
5-5I887
49.965
5.80108
49.921
0.6
4.76042
54-6o3
5.00281
54-546
5-25772
54494
5.52578
54-447
5.80765
54405
0.65
4.76802
59.064
5.01005
59.011
5.26461
58.962
5-53233
58.919
5.81389
58.879
0.7
4-77503
63.512
5.01672
63463
5.27096
63.419
5-53837
63.380
5.81964
63-344
0-7S
4.78127
67.947
5.02265
67.904
5.27662
67.866
5-54375
67.831
5.82476
67.800
0.8
4.78661
72.371
5-02773
72.336
5.28143
72.304
5-54834
72.275
5-82913
72.249
0.85
4.79088
76.786
5-03181
76.759
5-28531
76.735
5-55204
76.712
5-83265
76.692
0.9
4.79402
81.195
5-03479
81.176
5.28816
81.160
5-55474
81.144
5-83522
81. 131
0-95
4-79593
85-599
5.03661
85-589
5.28989
85.581
5-55639
85-573
5-83680
85.566
1.0
4-79657
90.000
5.03722
90.000
5.29047
90.000
5-55695
90.000
5-83732
90.000
1.05
4-79593
94.401
5.03661
94.411
5.28989
94.419
5-55639
94.427
5-83680
94434
1.1
4.79402
98.805
5-03479
98.824
5.28816
98.840
5-55474
98.856
5-83522
98.869
MS
4.79088
103.214
5-03181
103.241
5-28531
103.265
5-5S204
103.288
5-83265
103.308
1.2
4.78661
107.629
5-02773
107.664
5.28143
107.696
5-54834
107.725
5-82913
107.751
1-25
4.78127
112.053
5.02265
112.096
5.27662
112. 134
5-54375
112. 169
5.82476
112.200
i-3
4-77503
116.488
5.01672
116.537
5.27096
116.581
5-53837
116.620
5.81964
116.656
i-35
4.76802
120.936
5.01005
120.989
5.26461
121.038
5-53233
1 2 1. 081
5.81389
121. 121
i-4
4.76042
125-397
5.00281
125.454
5-25772
125.506
5-52578
125.553
5.80765
125-595
i-45
4.75240
129.873
4.99518
129.932
5.25046
129.986
5-51887
130-035
5.80108
130.079
i-5
4-74415
I34-364
4-98734
134.424
5.23728
134479
5-5"77
I34-529
5-79434
134-573
i-55
4-73592
138.870
4-97950
138.930
5-23553
138.984
5.50468
I39-034
5-78758
139.078
1.6
4.72784
143-392
4.97183
14345 1
5.22825
I43-503
549775
143-551
5.78099
143-593
1. 65
4.72017
I47-930
4.96454
147.984
5.22131
148.034
549 i:t 5
148.078
5-77472
148. 1 19
i-7
4.71308
152.482
4.95780
152.531
5.21490
152.576
548505
152.617
5.76982
152.653
i-75
4.70675
157.046
4-95177
157.090
5.20917
157.129
5.47961
I57-I65
5-76375
I57.I97
1.8
4.70134
161.622
4.94662
161.659
5.20428
161.691
547495
161. 721
5-75932
161.748
1.85
4.69697
166.208
4.94249
166.236
5-20035
166.261
5.47122
166.284
5.75576
166.305
1.9
4-69377
170.801
4-93944
170.820
5-19745
170.837
5.46847
170.853
5.753i6
170.867
i-9S
4.69182
175-399
4-93759
175.409
5-I9569
175.418
5.46679
175.426
5.75I56
175433
2.0 4.69117 180.000 4.93696 180.000 5.19510 180.000 5.46623 180.000 5.75103 180.000
Example. sinh (2.40 4- ioj) = 5-49775 /36-449 = 549775 /36.26'.56".
[99]
Table X. HYPERBOLIC SINES, sinh (x + iq) -r/y. Continued
x = 2.5
x = 2.55
X = 2.6
x = 2.65
x = 2.7
6.05020
0.000
6.36451
0.000
6.69473
0.000
7.04169
0.000
7.40626
0.000
0.05
6.05071
4.561
6.36499
4-555
6.69518
4-55Q
7.04213
4-545
7.40668
4-54Q
O.I
6.05223
9.120
6.36644
9.109
6.69656
9.098
7-Q4343
9.089
7.40791
9.080
0.15
6.05471
13.676
6.36879
13.660
6.69880
13.644
7-04556
13-631
7.40994
13.618
0.2
6.05808
18.228
6.37201
18.206
6.70185
18.187
7.04847
18.169
7-41271
18.153
0.25
6.06229
22.774
6.37601
22.748
6.70565
22.725
7.05208
22.703
7.41614
22.684
o-3
6.06722
27-3I4
6.38068
27.284
6.71011
27.257
7-05631
27.232
7.42017
27.210
o-3S
6.07273
31-845
6.38592
31.812
6.71509
31.782
7.06105
3I-756
7.42467
3I-73I
0.4
6.07869
36.368
6.39160
36.333
6.72048
36.301
7.06618
36.273
742955
36.246
0-4S
6.08496
40.882
6-39755
40.845
6.72616
40.813
7.07158
40.783
7.43468
40.756
0.5
6.09139
45-386
6.40367
45-35
6.73197
45-3i6
7.07711
45.286
7-43994
45-259
o.55
6.09781
49.881
6.40977
49.845
6.73778
49.812
7.08264
49.782
7-445I9
49-755
0.6
6.10406
54-366
6.41572
54-332
6-74343
54-300
7.08802
54-272
7-45032
54.246
0.65
6.10999
58.843
6.42137
58.810
6.74881
58.781
7-093I3
58.754
7-455I8
58.730
0.7
6.11547
63.311
6.42658
63.282
6.75376
63-255
7.09784
63.230
7.45966
63.209
o-75
6.12034
67.772
6.431 21
67.746
6.75818
67.722
7.10204
67.701
7.46366
67.682
0.8
6.12450
72.226
6.43518
72.204
6.76195
72.185
7-10563
72.167
7.46708
72.152
0.85
6.12785
76.674
6.43836
76.658
6.76499
76.643
7-10851
76.629
7.46982
76.617
0.9
6113030
81. 119
6.44069
81.107
6.76720
81.097
7.11062
81.088
7-47i83
81.080
0-9S
6.13179
85.560
6.44212
85-554
6.76855
85-549
7.11191
85-544
7.47306
85-540
1. 00
6.13229
90.000
6.44259
90.000
6.76901
90.000
7.11234
90.000
7-47347
90.000
1.05
6.13179
94.440
6.44212
94.446
6.76855
94-451
7.11191
94.456
7.47306
94.460
1.1
6.13030
98.881
6.44069
98.893
6.76720
98.903
7.11062
98.912
7-47i83
98.920
MS
6.12785
103.326
6.43836
103.342
6.76499
103.357
7-10851
103.371
7.46982
103.383
1.2
6.12450
107.774
6.43518
107.796
6.76195
107.815
7.10563
107.833
7.46708
107.848
1-25
6.12034
112.228
6.43121
112.254
6.75818
112.278
7.10204
112.299
7.46366
112.318
i-3
6.11547
116.689
6.42658
116.718
6.75376
116.745
7.09784
116.770
7.45966
116. 791
i-3S
6.10999
121. 157
6.42137
121. 190
6.74881
121. 219
7-093 J 3
121.246
7-455i8
121.270
1.4
6.10406
125.634
6.41572
125.668
6-74343
125.700
7.08802
125.728
7-45032
125.754
1 -45
6.09781
130.119
6.40977
I30-I55
6.73778
130.188
7.08264
130.218
7-445I9
130.245
i-5
6.09139
134.614
6.40367
134-651
6.73197
134.684
7.07711
I34-7I3
743994
134-741
1-55
6.08496
139.118
6-39755
139-155
6.72616
139.187
7.07158
139.217
7.43468
139.244
1.6
6.07869
143.632
6.39160
143.667
6.72048
143.699
7.06618
I43-727
742955
143-754
1.65
6.07273
148.155
6.38592
148.188
6.71509
148.218
7.06105
148.244
7.42467
148.269
i-7
6.06722
152.686
6.38068
152.716
6.71011
152.743
7.05631
152.768
7.42017
152.790
i-7S
6.06229
157.226
6.37601
157-252
6.70565
157-275
7.05208
157.297
7.41614
I57-3I6
1.8 .
6.05808
161.772
6.37201
161.794
6.70185
161.813
7.04847
161.831
7.41271
161.847
1.85
6.05471
166.324
6.36879
166.340
6.69880
166.356
7.04566
166.369
7.40994
166.382
1.9
6.05223
170.880
6.36644
170.891
6.69656
170.902
7-04343
1 70.91 1
7.40791
170.920
i-95
6.05071
175-439
6.36499
175-445
6.69518
I75-450
7.04213
175-455
7.40668
i7546o
2.0 6.05020 180.000 6.36451 180.000 6.69473 180.000 7.04169 180.000 7.40626 180.000
Example. sinh (2.6 + i ojS) = 6.74343 /54.3qo = 6.74343 /54.i8W.
[100]
Table X. HYPERBOLIC SINES, sinh (x +iq) - r./y. Cgnti^ued
x = 2.75
* = 2.8
x - 2.85
x = 2.9
x = 2.95
7-78935
0.000
8.19192
0.000
8.61497
0.000
9-05956
0.000
9.52681
0.000
0.05
7-78975
4-537
8.19230
4-533
8.61532
4-530
9.05990
4-527
9-527I3
4-525
O.I
7.79092
9-Q73
8.19341
9.066
8.61639
9.060
9.06091
9-054
9.52809
9.049
0.15
7.79285
13.607
8.19524
I3-596
8.61813
I3-587
9.06257
13-579
9.52967
I3-57I
0.2
7-79547
18.138
8.19774
18.125
8.62051
18.113
9.06483
18.102
9.53182
18.093
0.25
7-79875
22.666
8.20085
22.650
8.62347
22.636
9.06764
22.623
9-53450
22.611
-3
7.80257
27.190
8.20449
27.172
8.62691
27-155
9.07093
27.141
9-53762
27.127
o-3S
7.80685
31.709
8.20857
31.689
8.63080
31.671
9.07461
3I-655
9-54II3
31.640
0.4
7.81149
36.223
8.21298
36.202
8.63500
36.183
9.07861
36-165
9.54492
36.150
o-45
7.81637
40-73I
8.21762
40.710
8.63941
40.690
9.08281
40.671
9.54892
40.655
-5
7.82138
45-234
8.22238
45.212
8.64395
45.192
9.08711
45-173
9-55301
45-157
o.55
7.82638
49-731
8.22713
49.709
8.64846
49.689
9.09142
49.671
9-557H
49.655
0.6
7-83125
54.222
8.23177
54.201
8.65287
54.182
9.09561
54-i65
9.56109
54-149
0.65
7-83588
58.708
8.23617
58.688
8.65706
58.670
9.09959
58.654
9.56488
58.640
0.7
7.84015
63.189
8.24024
63.171
8.66092
63-I55
9.10327
63.140
9-56838
63.127
o.75
7-84395
67.665
8.24385
67.649
8.66436
67.636
9.10655
67.622
9-57I50
67.611
0.8
7.84720
72.137
8.24694
72.124
8.66731
72.112
9.10934
72.102
9.57416
72.092
0.85
7.84980
76.606
8.24942
76.596
8.66967
76.587
9.11160
76.579
9-57630
76.571
0.9
7.85172
81.072
8.25124
81.065
8.67140
81.059
9.11324
81.053
9-57787
81.048
o-95
. 7.85288
85-536
8.25235
8-5-533
8.67246
85-530
9.1 1424
85-527
9.57882
85-524
1.0
7-85328
90.000
8.25273
90.000
8.67281
90.000
9.11458
90.000
9-57915
90.000
1. 05
7.85288
94.464
8.25235
94.467
8.67246
94.470
9.11424
94-473
9-57882
94.476
1.1
7.85172
98.928
8.25124
98-935
8.67140
98.941
9.11324
98.947
9-57787
98.952
i-i5
7.84980
103.394
8.24942
103.404
8.66967
103.413
9.11160
103.421
9-57630
103.429
1.2
7.84720
107.863
8.24694
107.876
8.66731
107.888
9.10934
107.898
9.57416
107.908
1-25
7-84395
112.335
8.24385
112.351
8.66436
112.364
9.10655
112.378
9-57i5o
112.389
i-3
7.84015
116.811
8.24024
116.829
8.66092
116.845
9.10327
116.860
9-56838
116.873
i-3S
7-83588
121.292
8.23617
121.312
8.65706
121.330
9.09959
121.346
9.56488
121.360
1.4
7-83125
125.778
8.23177
125.799
8.65287
125.818
9.09561
I25-835
9.56109
125.851
i-4S
7.82638
130.269
8.22713
130.291
8.64846
1 30.3 1 1
9.09142
130.329
9-557"
130.345
i-5
7.82138
134.766
8.22238
134.788
8.64395
134.808
9.0871 1
134.827
9-55301
I34.843
i-5S
7.81637
139.269
8.21762
139.290
8.63941
139.310
9.08281
I39-329
9.54892
139-345
1.6
7.81 149
143-777
8.21298
143.798
8.63500
143.817
9.07861
I43-835
9-54492
143.850
1.65
7.80685
148.291
8.20857
148.31 1
8.63080
148.329
9.07461
148.345
9-54"3
148.360
i-7
7.80257
152.810
8.20449
152.828
8.62691
152.845
9.07093
152.859
9-53762
152-873
1-75
7-79875
157-334
8.20085
I57-350
8.62347
I57-364
9.06764
157-377
9-53450
I57-389
1.8
7-79547
161.862
8.19774
161.875
8.62051
161.887
9.06483
161.898
9.53182
161.907
1.85
7-79285
166.393
8.19524
166.404
8.61813
166.413
9-06257
166.421
9.52967
166.429
1.9
7.79092
170.927
8.19341
170.934
8.61639
1 70.940
9.06091
170.946
9.52809
170.951
1 -95
7-78975
I75-463
8.19230
I75-467
8.61532
i75-47o
9.05990
175-473
9-527I3
175-475
2.0 7.78935 180.000 8.19192 180.000 8.61497 180.000 9.05956 180.000 9.52681 180.000
Example. sinh (2.95 + i 1.95) = 9-5 2 7i3 /i75-475' = 9-52713 /i75-28'.3o"
[101]
Table X.. HYPERBOLIC SINES, sinh (x + iq) = r /y. Continued
x = 3.0
x = 3.05
* = 3-i
x = 3-i5
x = 3.2
10.01787
0.000
iQ-53399
0.000
c 1.07645
0.000
1 1. 6466 1
0.000
12.24588
0.000
0.05
10.01820
4-522
10.53430
4.520
1 1.07670
4.518
[ 1.64690
4.516
12.24610
4-515
O.I
10.01910
9.044
10.53520
9.040
[1.07750
9.036
[1.64770
9-033
12.24690
9.030
0.15
10.02060
13-565
10.53660
13-559
[ 1.07890
13-553
1 1.64890
I3-548
12.24810
13-543
0.2
10.02260
18.084
10.53850
18.076
[ 1.08080
18.068
[i. 65070
18.062
12.24980
18.056
0.2s
10.02520
22.601
10.54090
22.591
[i. 083 10
22.583
[i. 65 290
22.575
12.25180
22.568
-3
10.02820
27.115
10.54380
27.104
[ 1.08580
27.094
1-65540
27.085
12.25430
27.077
o-3S
10.03150
31.627
10.54690
3i-6i5
[ 1.08880
31.604
ti.65830
3*-594
12.25700
3I-585
0.4
10.03510
36.135
10.55040
36.122
[ 1.09200
36-111
[1.66140
36.100
12.26000
36.091
0-4S
10.03890
40.640
10.55400
40.627
[ 1.09540
40.615
[ 1.66470
40.604
12.26310
40.594
o-5
10.04280
45.142
10.55770
45-129
1 1.09900
45.116
n.66810
45-105
12.26630
45-095
o-5S
10.04670
49.640
10.56140
49.627
[i. 10250
49.615
[1.67140
49.604
12.26950
49-594
0.6
10.05050
54-135
10.56500
54.122
[i. 10600
54.110
[1.67470
54.100
12.27260
54.090
0.65
10.05410
58.626
10.56840
58.614 i
1. 109 20
58.604
[1.67780
58.594
12.27550
58.585
0.7
10.05743
63.114
10.57160
63.104 !
H.11220
63.094 ]
[ 1 .68060
63.085
12.27820
63.077
o.75
10.06040
67.600
10.57440
67.591 ]
n.11490
67.582 i
1 1.683 20
67-574
12.28070
67.567
0.8
10.06292
72.083
10.57680
72.075
n.11720
72.068 i
c 1.68540
72.062
12.28280
72.056
0.85
10.06500
76.564
10.57880
76.558 I
n.11900
76.553 I
[1.68710
76.548
12.28440
76.543
0.9
10.06645
81.044
10.58020
81.040
[i. 12040
81.036 ]
1 1.68840
81.032
12.28560
81.029
o-95
10.06737
85.522
10.58110
85.520 ]
ti.12120
85.518 .
1 1.68920
85.516
12.28640
85.5I5
1.0
10.06766
90.000
10.58135
90.OOO ]
1.12150
90.000 ]
1.68946
90.000
12.28665
90.000
1.05
10.06737
94.478
10.58110
94.480 ]
1.12120
94.482 ]
: 1.68920
94.484
12.28640
94.485
1.1
10.06645
98.956
10.58020
98.960 ]
1 . 1 2040
98.964 ]
1 1.68840
98.968
12.28560
98.971
iiS
10.06500
103.436
10.57880
103.442 1
1.11900
103.447 ]
1.68710
103.452
12.28440
103.457
1.2
10.06292
107.917
10.57680
107.925 ]
1.11720
107.932 ]
[ 1.68540
107.938
12.28280
107.944
1-25
10.06040
112.400
10.57440
112.409 ]
1.1 1490
112.418 ]
1.68320
112.426
12.28070
"2.433
i-3
10.05743
116.886
10.57160
116.896 ]
1.11220
116.906 ]
1.68060
116.915
12.27820
116.923
i-35
10.05410
121.374
10.56840
121.386 ]
1. 10920
121.396 3
1.67780
121 .406
12.27550
121.415
1.4
10.05050
125.856
10.56500
125.878 ]
1. 10600
125.890 ]
1.67470
125.900
12.27260
125.910
i-45
10.04670
130.360
10.56140
130.373 3
1. 10250
130.385 1
1. 6 7 140
130.396
12.26950
130.406
i-5
10.04280
I34-858
10.55770
134.871 :
[ 1.09900
I34.884 ]
[I.66810
I34.895
12.26630
I34.905
i-SS
10.03890
139.360
10.55400
139-373 J
1.09540
I39-385 ^
1.66470
I39-396
12.26310
139.406
1.6
10.03510
143.865
10.55040
143-878 ]
1.09200
I43.889 ]
1. 66 1 40
143.900
12.26000
143.909
1.65
10.03150
148.373
10.54690
148.385 l
1.08880
148.396 1
1.65830
148.406
12.25700
148.415
i-7
10.02820
152.885
10.54380
152.896 ]
1.08580
152.906 ]
1.65540
I52-9I5
12.25430
152.923
i-75
10.02520
157-399
10.54090
157.409
ti.08310
I57-4I7 1
[1.65290
I57-425
12.25180
157432
1.8
10.02260
161.916
10.53850
161.924 ]
[ 1.08080
161.93I ]
[ 1.65070
161.938
12.24980
161.944
1.8S
10.02060
166.435
10.53660
166.441 ]
1.07890
166.447 ]
1.64890
166.452
12.24810
166.457
1.9
10.01910
170.956
10.53520
170.960 i
[1-07750
170.964 ]
1.64770
170.967
12.24690
170.970
1 -95
10.01820
I75-478
10.53430
175.480 :
1.07670
175.482 ]
1.64690
175.484
12.24610
I75-485
2.0
10.01787
180.000
io.53399
180.000 ]
1.07645
180.000 :
1.6466 1
180.000
12.24588
180.000
Example. sinh (3.2 + i i^i) = 12.28560 /98.97i = 12.28560 /98.58'.i6 g .
[102]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r
Continued
x = 3.25
* = 3-3
x = 3-35
x = 3-4
x = 3-45
12.87578
0.000
I3-53788
0.000
14.23382
0.000
14.96536
0.000
15-73432
0.000
0.05
12.87600
4-514
[3-538io
4.512
14.23403
4-5"
14.96556
4.510
I5-73450
4-509
O.I
[2.87670
9.027
t3-53878
9.024
14.23470
9.022
14.96616
9.020
I5-735IO
9.018
0.15
[2.87790
13-539
13-53991
I3-536
14-23573
13-532
14.96716
13-529
I5-736o3
13-526
0.2
[2.87949
18.051
I3-54I4I
18.046
14.23718
18.041
14.96855
18.038
I5-73736
18.034
0.25
[2.88146
22.561
t3-54322
22.555
14.23897
22.550
14-97023
22-545
I5-73898
22.541
o-3
[2.88380
27.070
E3-54550
27.063
14.24106
27.057
14.97225
27.052
15.74088
27.047
-35
[2.88637
31-577
t3-54796
31-569
14.24339
31-563
14.97448
31-557
15.74300
3i-55i
0.4
12.88910
36.082
[3.55062
36.074
14.24595
36.067
14.97690
36.061
I5-74529
36.055
o.45
[2.89215
40.585
[3-55346
40.577
14.24863
40.570
14-97945
40-563
15-74772
40.557
0.5
[2.89518
45.086
[3-55633
45.078
14-25137
45-071
14.98205
45.064
15.75020
45-058
o-55 1
[2.89820
49-585
[3-559I8
49-577
14.25412
49-570
14.98466
49-563
I5-75270
49-557
0.6 ]
2.901 1 7
54.082
13-56203
54-Q74
14.25614
54.067
14.98721
54.061
I5-755IO
54-055
0.65 ]
2.90398
58.577 i
t3-56470
58.569
I4.25933
58.563
14.98960
58.557
I5-75740
58.551
0.7 3
2.90658
63.070 ]
[3.56718
63.063
14.26167
63-057
14.99186
63.052
I5-75950
63.047
0-75 ^
2.90888
67.561
[3-56936
67-555
14.26377
67-55o
14.99385
67-545
15.76144
67-541
0.8 ]
2.91085
72.051
[3-57I23
72.046
14.26556
72.041
14-99555
72.038
15-76303
72.034
0.85 i
2.91240
76-539 J
[3-57275
76.535
14.26700
76-532
14.99692
76.529
I5-76433
76.526
0.9 ]
2.91360.
81.027 ]
[3-57387
81.024
14.26805
81.022
14.99790
81.020
I5-76530
81.018
0.95 ]
2.91430
85-514 1
3-57455
85.512
14.26870
85-5"
I4.99853
85.510
15-76587
85-509
I.O ]
2.91456
90.000
[3.57476
90.000
14.26891
90.000
14-99874
90.000
15.76607
90.000
1.05 1
2.91430
94.486 i
3-57455
94.488
14.26870
94.489
I4.99853
94.490
15-76587
94.491
1.1 ]
2.91360
98.973 :
3-57387
98.976
14.26805
98.978
14.99790
98.980
I5-76530
98.982
1. 15 )
2.91240
103.461 i
3-57275
103.465
14.26700
103.468
14.99692
103.471
I5-76433
103.474
1.2 ]
2.91085
107.949 ]
[3-57I23
107.954
14.26556
107.959
14-99555
107.963
15-76303
107.966
1. 25 ]
2.90888
112.439 3
3-56936
112.445
14.26377
112.450
14.99385
112.455
15.76144
112.459
i-3 >
2.90658
116.930 ]
3-56718
116.937
14.26167
116.943
14.99186
116.948
I5-75950
"6.953
i-35 ]
2.90398
121.423 ]
[3-56470
121.431
I4.25933
121.437
14.98960
121.443
I5-75740
121.449
1.4 l
2.901 1 7
125.918 i
3-56203
125.926
14.25614
125-933
14.98721
125.939
I5-755IO
125.945
1-45 3
2.89820
130.415 ;
[3-559I8
130.423
14.25412
130.430
14.98466
130.437
15.75270
130.443
i-5 >
2.89518
134-9*4 1
[3-55633
134.922
14-25137
134.929
14.98205
I34.936
15.75020
134.942
i-55 1
2.89215
I39-4I5 ^
[3-55346
I39-423
14.24863
139-430
14-97945
139-437
15-74772
139-443
1.6 ]
2.88910
143.918 ]
[3.55062
143.926
14.24595
143-933
14.97690
143-939
I5-74529
143-945
1. 65 ]
2.88637
148.423 ]
t3-54796
148.431
14.24339
148.437
14.97448
148.443
15.74300
148.449
1.7 ]
2.88380
152.930 ]
3-54550
I52-937
14.24106
152.943
14.97225
152.948
I5.74088
J52-953
i75 1
2.88146
157-439 ]
3-54322
157-445
14.23897
I57450
14.97023
157-455
I5-73898
157-459
1.8 ]
2.87949
161.949 ]
[3-54I4I
161.954
14.23718
161.959
14.96855
161.962
I5-73736
161.966
1.85 1
2.87790
166.461 ]
3-53991
166.464
I4.23573
166.468
14.96716
166.471
15-73603
166.474
1.9 ]
2.87670
170.973 3
3-53878
170.976
14.23470
170.978
14.96616
170.980
I5-735IO
170.982
i-95 i
2.87600
175.486 ]
[3-538io
175488
14.23403
175.489
14.96556
I75-490
IS-73450
I75-49I
2.0 ]
2.87578
180.000 ]
3-53788
180.000
14.23382
180.000
14.96536
180.000
15-73432
180.000
Example. si
nh (3.3 + i 14) =
13.56718/
[i6.937 =
13-56718/
'n6.56'.]
3*-
[ 103 -j
Table X. HYPERBOLIC SINES, sinh (x + iq) =r /y. Continued
x = 3-5
x = 3-55
x = 3.6
3-65
m 3.7
O
O.OS
O.I
0.15
0.2
0.25
-3
o-3S
04
0-4S
o-5
o-55
0.6
0.65
0.7
o-75
0.8
0.85
0.9
-95
1.0
1.05
1.1
"5
1.2
1. 25
i-3
i-35
1.4
i-4S
i-5
i-5S
1.6
1.65
i-7
i-7S
1.8
1.85
1.9
i-95
2.0
6.54263
6.54281
6-54337
6.54428
6.54550
6.54702
6.54885
6.55087
6.55307
6.55538
6-55774
6.56010
6.56240
6.56460
6.56660
6.56840
6.56996
6.57120
6.57210
6.57260
6.57282
6.57260
6.57210
6.57120
6.56996
6.56840
6.56660
6.56460
6.56240
6.56010
6-55774
6.55538
6.55307
6.55087
6.54885
6.54702
6.54550
6.54428
6-54337
6.54281
0.000
4.508
9.016
13-524
18.031
22.537
27.042
31-547
36.050
40.552
45-052
49-552
54-050
58.547
63.042
67-537
72.031
76.524
81.016
85.508
90.000
94.492
98.984
103.476
107.969
112.463
116.958
121.453
125.950
130.448
134.948
139.448
143-950
148.453
152.958
157-463
161.969
166.476
170.984
175.492
7.39230
7.39248
7.39300
7.39386
7.39504
7-39650
7.39822
7.40015
7.40222
7.40441
7.40665
7.40900
7.41110
7.41310
7.41510
7.41680
7.41830
741945
7.42030
7.42083
7.42102
7.42083
7.42030
7.4I945
7.41830
7.41680
7.41510
7.41310
7.41 1 10
7.40900
7.40665
7.40441
7.40222
7.40015
7.39822
7-39650
7-38504
7.39386
7.39300
7.39248
0.000
4-507
9.015
13.522
18.028
22.534
27.038
3L542
36.045
40-547
45-047
49-547
54-045
58.542
63.038
67-533
72.028
76.521
81.015
85-507
90.000
94-493
98.985
103.479
107.972
112.467
116.962
121.458
125-955
130.453
134-953
139-453
143-955
148.458
152.962
157.466
161.972
166.478
170.985
175-493
8.28546
8.28560
8.28611
8.28694
8.28805
8.28942
8.29109
8.29292
8.29490
8.29699
8.29912
8.30126
8.30335
8.30530
8.30715
8.30880
8.31020
8.31130
8.31210
8.31260
8.31278
8.31260
8.31210
8.3 1 130
8.31020
8.30880
8.30715
8.30530
8.30335
8.30126
8.29912
8.29699
8.29490
8.29292
8.29109
8.28942
8.28805
8.28694
8.28611
8.28560
0.000
4-507
9.013
I3-5I9
18.025
22.530
27-035
3I-538
36.041
40.542
45-043
49.542
54.041
58.538
63-035
67-530
72.025
76.519
81.013
85-507
90.000
94-493
98.987
103.480
107.975
112.470
116.965
121.462
125.959
130.458
134-957
139458
143-959
148.462
152.965
157470
161.975
166.481
170.987
175493
9.22434
9.22448
9.22496
9.22577
9.22681
9.22813
9.22968
9.23142
9-23331
9-23530
9.23732
9.23940
9.24134
9-24323
9.24496
9.24650
9.24790
9.24890
9.24970
9-25015
9-25033
9-25015
9.24970
9.24890
9.24790
9.24650
9.24496
9-24323
9.24134
9.23940
9-23732
9-23530
9-23331
9.23142
9.22968
9.22813
9.22681
9.22577
9.22496
9.22448
0.000
4.506
9.012
I3-5I8
18.023
22.527
27.031
31-535
36.037
40.538
45-039
49.538
54-037
58.535
63-031
67.527
72.023
76.518
81.012
85.506
90.000
94.494
98.988
103.482
107.977
112.473
116.969
121.465
125.963
130.462
134.961
139.462
143-963
148.465
152.969
157473
161.977
166.482
170.988
175494
20.21129
20.21140
20.21189
20.21268
20.21365
20.21490
20.21639
20.21804
20.21981
20.22170
20.22365
20.22560
20.22750
20.22930
20.23090
20.23240
20.23365
20.23460
20.23540
20.23585
20.23601
20.23585
20.23540
20.23460
20.23365
20.23240
20.23090
20.22930
20.22750
20.22560
20.22365
20.22170
20.21981
20.21804
20.21639
20.21490
20.21365
20.21268
20.21189
20.21140
0.000
4.506
9.01 1
13-516
18.021
22.525
27.028
3I.53I
36.033
40.535
45-035
49-535
54-033
58.531
63.028
67-525
72.021
76.516
81.011
85.506
90.000
94.494
98.989
103.484
107.979
112.475
116.972
121.469
125.967
130.465
134-965
139.465
143.967
148.469
152.972
157475
161.979
166.484
170.989
175494
16.54263 180.000 17.39230 180.000 18.28546 180.000 19.22434 180.000 20.21129 180.000
Example. sinh (3.65 4- i 0.25) = 19.22813 /22.527 = 19.22813 j 22 .?,\' .57* .
[ 104]
Table X. HYPERBOLIC SINES, sinh (x + iq) = r [y. Continued
x - 3-75
x - 3.8
* = 3-85
* = 3-9
x = 3-95
0.05
0.1
0.15
0.2
0.25
-3
o-3S
0.4
o.45
0.5
o-55
0.6
0.65
0.7
-75
0.8
0.85
0.9
o-9S
1.0
1.05
1.1
i-i5
1.2
I-2S
i-3
i-3S
1.4
i-45
i-5
i-55
1.6
1.6s
i-7
i-75
1.8
1.85
1.9
1-95
21.24878
21.24891
21-24935
21.25006
21.25102
21.25221
21.25362
21.25520
21.25685
21.25869
21.26052
21.26236
21.26415
21.26586
21.26745
2I.2C
2I.27000
2I.27IOO
2I.27I70
21.27212
O.OOO
4-505
9.OIO
I3-5I4
18.OI9
22.522
27.026
3I-528
36.O3O
40-53I
45-032
49-531
54-030
58.528
63.026
67.522
72.019
76-5I4
81.010
85-505
21.27230 90.000
21.27212 94.495
21.27170 98.990
21.27100 103.486
21.27000 107.981
21.26885 112.478
21.26745 116.974
21.26586 121.472
21.26415 125.970
21.26236 130.469
21.26052
21.25869
21.25685
21.25520
21.25362
21.25221
21.25102
21.25006
21.24935
21.24891
134.968
139.469
143.970
148.472
152.974
I57-478
161.981
166.486
170.990
175-495
22.33941
22.33952
22-33995
22.34061
22.34153
22.34270
22.34401
22.34550
22.34712
22.34883
22.35060
22.35230
22.35403
22.35565
22.35716
22.35850
22.35962
22.36055
22.36122
22.36163
22.36178
22.36163
22.36122
22.36055
22.35962
22.35850
22.35716
22.35565
22.35403
22.35230
22.35060
22.34883
22.34712
22.34550
22.34401
22.34270
22.34153
22.34061
22-33995
22.33952
0.000
4-504
9.009
I3-5I3
18.017
22.520
27.023
31-526
36.027
40.528
45.029
49.528
54.027
58.526
63.023
67.520
72.017
76.513
81.009
85-504
90.000
94.496
98.991
103.487
107.983
112.480
116.977
121.474
125-973
130.472
134-971
139.472
143-973
148.474
152.977
157.480
161.983
166.487
170.991
175.496
23.48589
23.48601
23.48640
23.48704
23.48791
23.48900
23.49028
23-49I 15
23.49322
23.49486
2349652
23.49820
23.49980
23-50136
23.50277
23.50404
23.50512
23.50600
23.50664
23.50702
23-50717
23.50702
23.50664
23.50600
23.50512
23.50404
23.50277
23.50136
23.49980
23.49820
23.49652
23.49486
23.49322
2349 IJ 5
23.49028
23.48900
23.48791
23.48704
23.48640
23.48601
0.000
4-504
9.008
13-512
18.015
22.518
27.021
3I-523
36.025
40.526
45.026
49.526
54-025
58.523
63.021
67.518
72.015
76.512
81.008
85-504
90.000
94.496
98.992
103.488
107.985
112.482
116.979
121.477
125-975
130.474
134-974
139474
143-975
148.477
152.979
157.482
161.985
166.488
170.992
175.496
24.69110
24.69120
24.69159
24.69223
24.69302
24.69406
24.69528
24.69662
24.69809
24.69964
24.70121
24.70280
24.70440
24.70580
24.70720
24.70840
24.70940
24.71024
24.71690
24.71120
24-7II3S
24.71120
24.71090
24.71024
24.70940
24.70840
24.70720
24.70580
24.70440
24.70280
24.70121
24.69964
24.69809
24.69662
24.69528
24.69406
24.69302
24.69223
24.69159
24.69120
0.000
4-504
9.007
i3-5ii
18.014
22.517
27.019
3i-52i
36.022
40.523
45-023
49-523
54.022
58.521
'63.019
67-5I7
72.014
76.511
81.007
85-504
90.000
94.496
98.993
103.489
107.986
112.483
116.981
121.479
125.978
130.477
134.976
139477
143.978
148.479
152.981
157483
161.986
166.489
170.993
175.496
25.95806
25.95820
25-95854
25-959"
25.9599I
25.96090
25.96205
25-96333
25.96471
25.96618
25.96770
25.96920
25.97066
25.97206
25-97337
25.97450
25.97550
25.97630
25.97680
25.97720
25.9773I
25.97720
25.97680
25-97630
25.97550
25.97450
25-97337
25.97206
25.97066
25.96920
25.96770
25.96618
25.96471
25-96333
25.96205
25.96090
25.9599I
25.959ii
25-95854
25.95820
0.000
4-503
9.007
13.510
18.013
22.515
27.017
3i.5i9
36.020
40.521
45.021
49-521
54.020
58.519
63.017
67-515
72.013
76.510
81.007
85-503
90.000
94.497
98.993
103.490
107.987
112.485
116.983
121.481
125.980
130.479
134-979
139479
143.980
148.481
152-983
157485
161.987
166.490
170.993
175497
2.0 21.24878 180.000 22.33941 180.000 23.48589 180.000 24.69110 180.000 25.95806 180.000
Example. sinh (3.90 + i 1.90) = 24.69159 /i7o,993 = 24.69159 /i7o -59 , -35" f
[105]
Table XI. HYPERBOLIC COSINES, cosh (x + iq) = r /y
x = 0.05
x = 0.15
0.05
O.I
0.15
0.2
0.25
0.3
o-3S
0.4
0-4S
0.5
0-5S
0.6
0.65
0.7
o.75
0.8
0.85
0.9
0-9S
1.0
1.05
I.I
1.2
1.25
i-3
i-35
1.4
i-4S
i-5
i-55
1.6
1.6s
i-7
i-75
1.8
1.85
1.9
1 -95
1 .00000
0.99692
0.98769
0.97237
0.95106
0.92388
0.89101
0.85264
0.80902
0.76041
0.70711
0.64945
0.58779
0.52250
0-45399
0.38268
0.30902
0.23345
0.15643
0.07846
0.00
0.07846
0.15643
0.23345
0.30902
0.38268
0.45399
0.52250
0.58779
0.64945
0.70711
0.76041
0.80902
0.85264
0.89101
0.92388
0.95106
0.97237
0.98769
0.99692
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
1.00125
0.99817
0.98895
0.97366
o.95237
0.92523
0.89237
0.85407
0.81053
0.76202
0.70803
0.65135
0.58989
0.52487
0.45672
0.38594
0.31304
0.23874
0.16424
0.09305
0.00
0.225
o.453
0.687
0.930
1.186
1.458
1-754
2.079
2-443
2.860
3-348
3-934
4.661
5.600
6.877
8.741
"755
17-507
32.407
0.05002 90.000
0.09305 147-593
0.16424 162.493
0.23874 168.245
6.31304 171.259
0.38594
0.45672
0.52487
0.58989
0-65135
0.70803
0.76202
0.81053
0.85407
0.89237
0.92523
o-95237
0.97366
0.98895
0.99817
173.123
174.400
175-339
176.066
176.652
177.139
177-557
177.921
178.246
178.542
178.814
179.070
I79-3I3
179-547
179-775
1.00500
1. 001 94
0.99275
0.97752
0.95632
0.92930
0.89662
0.85851
0.81520
0.76698
0.71417
0.65713
0.59626
0.53201
0.46491
o.39558
0.32485
0.25403
0.18576
0.12724
0.10017
0.12724
0.18576
0.25403
0.32485
o.39558
0.46491
0.53201
0.59626
0.65713
0.71417
0.76698
0.81520
0.85851
0.89662
0.92930
0.95632
0.97752
0.99275
1.00194
0.00
0.450
0.905
i-37i
1.855
2.364
2.907
3-495
4.142
4.866
5.692
6.656
7.811
9.238
11.068
I3-529
17-053
22.545
32.181
51.700
90.000
128.300
147.819
157-455
162.947
166.471
168.932
170.762
172.189
173-344
174.308
175-134
I75-858
176.505
177.093
177.636
178.145
178.629
179.095
I79-550
1.01127
1.00822
0.99909
0.98396
0.96290
0.93607
0.90364
0.86583
0.82291
0.77527
0.72296
0.66667
0.60676
o.54376
0.47831
0.41 1 24
0-34375
0.27779
0.21712
0.16978
0.15056
0.16978
0.21712
0.27779
0-34375
0.41 1 24
0.47831
o.54376
0.60676
0.66667
0.72296
0.77527
0.82291
0.86583
0.90364
0.93607
0.96290
0.98396
0.99909
1.00822
0.00
0.671
I-35I
2.047
2.769
3-529
4-338
5-213
6.174
7.247
8.468
9.889
11.581
13-656
16.289
19.771
24.618
31-805
43.229
62.139
90.000
117.861
136.771
148.195
I55-382
160.229
163. 711
166.344
168.419
1 70.1 1 1
I7I-532
172.753
173.826
174.787
175.662
176.471
177.231
177-953
178.649
179.329
1.02007
1. 01 704
1.00800
0.99300
0.97213
o.94556
0.91347
0.87609
0.83370
0.78661
0.73521
0.67994
0.62131
0-55995
0.49663
0.43242
0.36882
0.30827
0.25497
0.21608
0.00
0.890
1. 791
2.713
3.669
4.674
5-743
6.897
8.161
9-569
11. 165
13.012
15.198
I7-853
21.175
25-478
3 J -277
39.424
51-254
68.261
0.20134 90.000
0.21608 in. 739
0.25497 128.746
0.30827 140.576
0.36882 148.723
0.43242
0.49663
0-55995
0.62131
0.67994
0.73521
0.78661
0.83370
0.87609
0.91347
0.94556 175.326
0.97213 176.331
0.99300 177.287
1.00800 178.209
1. 01 704 1 79. 1 10
154-522
158.825
162.147
164.802
166.988
168.835
170.431
171-839
173.103
174-257
2.0 1.00000 180 1.00125 180.000 1.00500 180.000 1.01127 180.000 1.02007 180.000
Example. cosh (0.10 + i 0.55) = 0.65713 /6.656 = 0.65713 /6.39'.22 g .
[106]
Table XL HYPERBOLIC COSINES, cosh (* + iq) = r /y. Continued
x = 0.25
x = 0.3
x = 0.35
x = 0.4
x 0.45
1.03141
0.000
1 -04534
0.000
1. 06 1 88
0.000
1.08107
0.000
I. IO297
O.OOO
0.0s
1.02843
1. 104
1.04239
*-3*3
1.05898
1-516
1.07822
I-7I3
I.IOOI7
I.902
O.I
1. 01949
2.221
I-03357
2.642
1.05029
3-050
1.06970
3-444
I.O9182
3.823
o.is
1 .00464
3-365
1. 01 894
4.001
1.03590
4.617
I.05557
5-212
I.O7798
5-784
0.2
0.98403
4-550
0.99862
5407
1.01592
6.238
1-03597
7.O38
I.O5880
7.806
0.25
o.95779
5-793
0.97277
6.881
0.99052
7-932
1.01107
8-944
I.O3446
9-913
o-3
0.92612
7-U3
0.94161
8-443
0-95994
9.726
0.981 13
10.957
I.OO52I
12.132
0-3S
0.88927
8.536
0.90539
10.122
0.92444
11.647
0.94642
I3.IO7
O.97136
I4.496
0.4
0.84754
10.090
0.86443
11.951
0.88436
13-733
0.90732
I5-432
0.93330
17.O42
0-4S
0.80127
11.815
0.81912
13.972
0.84012
16.029
0.86426
17.979
O.89I49
I9.816
0.5
0.75088
13.762
0.76989
16.241
0.79220
18.592
0.81775
2O.804
O.84469
22.875
o.55
0.69685
16.001
0.71730
18.834
0.741 19
21.497
0.76844
23.982
O.79895
26.288
0.6
0.63977
18.629
0.66199
21.849
0.68781
24.843
0.71708
27.607
0.74969
3O.I44
0.65
0.58036
21.785
0.60476
25-425
0.63292
28.763
0.66462
3I.80O
O.69968
34-546
0.7
o.5i954
25-673
0.54666
29.758
0.57766
33-157
0.61223
36.712
O.65OI2
39.626
0-7S
0.45854
30.595
0.48906
35-118
0.52348
39.079
0.56140
42.529
O.60249
45-527
0.8
o-399 J 3
37.008
0.43385
41.878
0.47231
45.992
0.51401
49.464
O.55860
52-399
0.85
0.34396
45-057
0.38370
50.507
0.42671
54.484
0.47246
57-712
O.52062
60.358
0.9
0.29782
57.110
0.34235
61.467
0.38994
64.786
0-43953
67.37I
0.49093
69.424
o-95
0.26452
72.186
0.31447
74.882
0.36571
76.831
0.41818
78.297
O.47I9I
79433
1.0
0.25261
90.000
0.30452
90.000
o.357i9
90.000
0.41075
90.000
046534
90.000
1. 05
0.26452
107.814
0.31447
105. 118
0.36571
103.169
0.41818
IOI.703
O.4719I
100.567
1.1
0.29782
122.890
0.34235
118.533
0.38994
115-214
0-43953
II2.629
O.49O93
110.576
i-i5
o.34396
134-943
0.38370
129.493
0.42671
125.516
0.47246
122.288
O.52062
119.642
1.2
o-399!3
142.992
0.43385
138.122
0.47231
134.008
0.51401
130.536
0.55860
127.601
1. 25
0.45854
149.405
0.48906
144.882
0.52348
140.921
0.56140
I3747I
O.60249
134473
i-3
0.51954
i54.3 2 7
0.54666
150.242
0.57766
146.843
0.61223
143.288
O.65OI2
140.374
i-35
0.58036
158.215
0.60476
154-575
0.63292
I5L237
0.66462
I48.2OO
O.69968
145454
1.4
0.63977
161.371
0.66199
158.151
0.68781
I55.I57
0.71708
I52.393
0.74969
149.856
i-4S
0.69685
163.999
0.71730
161. 166
0.741 19
158.503
0.76844
I56.O18
O.79895
I53-7I2
i-5
0.75088
166.238
0.76989
163.759
0.79220
161.408
0.81775
I59.I96
O.84649
157.125
i-55
0.80127
168.185
0.81912
166.028
0.84012
163.971
0.86426
I62.02I
O.89149
160.184
1.6
0.84754
169.910
0.86443
168.049
0.88436
166.267
0.90732
164.568
0.93330
162.958
1.6s
0.88927
171.464
0.90539
169.878
0.92444
168.353
0.94642
166.893
O.97136
165.504
i-7
0.92612
172.887
0.94161
I7I.557
o.95994
170.274
0.981 13
169.O43
I.0052I
167.868
i-75
o.95779
174.207
0.97277
173.119
0.99052
172.068
1.01107
171.056
I.O3446
170.087
1.8
0.98403
I75-450
0.99862
174-593
1.01592
173.762
I-03597
I72.962
I.O5880
172.194
1.85
1.00464
176.635
1. 01 894
175-999
1.03590
I75-383
I-05557
174-788
I.07798
174.216
1.9
1. 01 949
177.779
I-03357
I77.358
1.05029
176.950
1.06970
176.556
I.O9182
176.177
i-9S
1.02843
178.896
1.04239
178.687
1.05898
178.484
1.07822
I78.287
I.IOOI7
178.098
2.0
1. 03 141
180.000
1 -04534
180.000
1. 06 1 88
180.000
1.08107
180.OOO
I. IO297
180.000
Example.
cosh (0.40 + i 0.5)
1 = 0.81775 /2O .8o4
= 0.81775 /20.48'
,I 4 \
[107]
Table XI. HYPERBOLIC COSINES, cosh (x + iq) = r
Continued
* = 0.5
x = 0.55
x = 0.6
0.65
0.7
1. 12763
0.000 .
i-i55io
0.000
1-18547
0.000
1. 21879
0.000
I-255I7
0.000
0.05
1.1 2489
2.083
1. 15244
2.256
1. 18287
2.420
1. 21626
2.576
1. 25271
2.723
O.I
1.11672
4.186
1. 1 4446
4-533
1.17510
4.879
1. 20871
5-174
I-24538
5468
o.is
1. 10320
6-33 1
1.13127
6.852
1. 16226
7-347
1.19623
7-8i5
1.23327
8.256
0.2
1 .08446
8-539
1.1 1300
9-237
1. 14448
9.898
1. 17892
10.523
1. 21653
II. no
0.25
1.06070
10.836
1.08987
XX.7X3
1. 12200
12.541
I-I57I5
13.322
1.19541
14.054
-3
1.03220
13-249
1.06214
14-307
1.09509
I5-304
1.13108
16.240
1.17019
17. 116
o.35
0.99927
15-811
1 .03004
17.052
1. 064 1 1
18.216
I.IOIII
19.306
1.14125
20.323
0.4
0.96232
18.559
0-99437
19.984
1.02948
2I-3IS
1.06769
22-555
1. 1 0904
23.706
o.4S
0.92182
21.538
0.95524
23.146
0.99174
24.640
1-03134
26.024
1.07409
27.302
-5
0.87837
24.803
0.91338
26.589
0.95149
28.238
0.99270
29-755
1.03704
31.148
-55
0.83266
28.416
0.86951
30.372
0.90946
32.162
0.95249
33-796
0.99861
35-284
0.6
0.78552
32458
0.82447
34-563
0.86650
36471
0.91156
38.197
0.95966
39-755
0.65
0.73793
37.020
0.77927
39-241
0.82361
41.231
0.87090
43.011
0.92112
44.603
0.7
0.69112
42.207
0.73510
44.489
0.78194
46.506
0.83160
48.290
0.88406
49.867
o-75
0.64652
48.129
o-69333
50.390
0.74282
52.358
0.79492
54-074
0.84965
55-574
0.8
0.60583
54.889
o.65555
57.010
0.70769
58.826
0.76220
60.387
0.81911
61.737
0.85
0.57100
62.547
0.62350
64-375
0.67810
65.914
0.73482
67.219
0.79369
68-335
0.9
0.54407
71.082
0.59894
72.441
o.65559
73-568
0.71409
74-514
C77455
75.3I5
o-95
0.52697
80.335
0.58345
81.064
0.64147
81.663
0.70115
82.161
0.76263
82.581
1.0
0.52110
90.000
0.57815
90.000
0.63665
90.000
0.69675
90.000
0.75858
90.000
1.05
0.52697
99.665
0.58345
98.936
0.64147
98.337
0.701 15
97-839
0.76263
97.419
1.1
0.54407
108.918
0.59894
107.559
0.65559
106.432
0.71409
105.486
o.77455
104.685
i-i5
0.57100
H7-453
0.62350
115.625
0.67810
114.086
0.734S2
112. 781
0.79369
1 1 1.665
1.2
0.60583
125. in
o-65555
122.990
0.70769
121. 174
0.76220
119-613
0.81911
118.263
1-25
0.64652
131.871
o-69333
129.610
0.74282
127.642
0.79492
125.926
0.84965
124.426
i-3
0.69112
137-793
0.73510
135-5"
0.78194
133494
0.83160
131-710
0.88406
130-133
i-3S
0.73793
142.980
0.77927
140.759
0.82361
138.769
0.87090
136.989
0.92112
135-397
1.4
0.78552
147.542
0.82447
145-437
0.86650
I43-529
0.91156
141.803
0.95966
140.245
i-45
0.83266
151-584
0.86951
149.628
0.90946
147.838
0.95249
146.204
0.99861
144.716
1.50
0.87837
I55-I98
0.91338
I534II
0.95149
151.762
0.99270
1 50.. 245
1.03704
148.853
i-S5
0.92182
158.462
0.95524
156.854
0.99174
i55-36o
1-03134
I53-976
1.07409
152.698
1.60
0.96232
161.441
o.99437
160.016
1.02948
158.685
1.06769
157-445
1. 1 0904
156.294
1.65
0.99927
164.189
1 .03004
162.948
1. 064 1 1
161.784
I.IOIII
160.694
1.14125
159.677
1.70
1.03220
166.751
1.06214
165.693
1.09509
164.696
1.13108
163.760
1.17019
162.884
1-75
1.06070
169.164
1.08987
168.287
1. 12200
167.459
1-15715
166.678
1.19541
165.946
1.8
1.08446
1 7 1. 461
1.11300
170.763
1. 1 4448
170.102
1. 1 7892
169.477
1. 21653
168.890
1.8s
1. 10320
173.669
1.13127
173.148
1. 16226
172.653
I. 19623
172.185
1.23327
171.744
1.9
1.11672
175.814
1. 1 4446
175467
1.17510
175. 121
1. 20871
174.826
I-24538
174-532
1 -95
1.1 2489
177.917
1. 15244
177-744
1. 18287
177.580
1. 21626
177.424
1. 25271
177.277
2.0 1. 12763 180.000 1.15510 180.000 1. 18547 180.000 1. 21879 180.000 1. 25517 180.000
Example. cosh (0.65 + i ix>) = 0.69675 /90
[108]
Table XI. HYPERBOLIC COSINES, cosh (x + iq) = r [y. Continued
x = 0.75
x = 0.85
x = 0.9
* = 0.95
1.29468
0.000
1-33743
0.000
I-38353
0.000
I-43309
0.000
1.48623
0.000
0.05
1.29230
2.862
I-335I3
2.992
1-38130
3-"3
1.43094
3.227
1. 484 1 5
3-332
O.I
1.28520
5-745
1.32825
6.004
1.37466
6.246
1.42452
6-473
1.47797
6.684
0.15
1.27346
8.670
1.31691
9.058
1.36369
9.420
I-4I395
9-758
1.46778
10.071
0.2
1.25726
1 1. 661
1.30124
12.175
1.34858
12.656
1-39937
13.10?
I-4537I
I3-5I6
0.25
1.23689
14.740
1. 28152
15-379
r-32955
15-974
1-38105
16.526
1. 4361 1
17.037
o-3
1. 21248
17-933
1.25802
18.693
1.30693
19.398
I-35927
20.051
1.41519
20.653
o-35
1. 18457
21.267
1-23115
22.143
1. 28107
22.952
1-33444
23.699
1.39136
24-387
0.4
I-I53 
