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World War II Technical Manual concerning Air Navigation Tables.
Transcript of TM 1-208 Air Navigation Tables
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< I. L K-r ft.
WAR DEPARTMENT TECHNICAL MANUAL
v^y
AIR NAVIGATION
TABLES
WAR DEPARTMENT i AUGUST 1944
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WA R DEPARTMENT TECHNICAL MANUAL
T M 1-208
This manual supersedes TM 1-208. 5 June 1942, including C 1, 17 October 1942
AIR NAVIGATION
TABLES
WA R DEPARTMENT 1 AUGUST 1944
United Stales Government Printing Office
Washington : 1944
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WAR DEPARTMENT,
WASHINGTON 25, D. C., 1 August 1944.
TM 1-208, Air Navigation Tables, is published for the information and
guidance of all concerned.
[A. O. 300.7 (6 May 44).]
BY ORDER OF THE SECRETARY OF WAR:
G. C. MARSHALL,
Chief of Staff
OFFICIAL:
J A. ULIO,
Major General,
The Adjutant General.
DISTRIBUTION:
Depts (10); Air Forces (10); AF Comds (10); B and H 1 (6); R 1 (4);
Bn 1 (4).
For explanation of symbols, see FM 21-6.
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. CONTENTS
Page
TABLE I. Natural trigonometric functions 1
II. Common logarithms of numbers 25
III. Meridional parts or increased latitudes..... .... 45
IV. Reduction of local civil time to standard meridian time, and
the reverse . 53
V. Altitude-pressure tablefeet-inches 54
VI. Conversion of millibars and inches of mercury 55
VII. Table of constants and equivalents 56
VIII. Length of a degree in latitude and longitude 60
IX. Conversion tables for thermometer scales 62
X. Logarithms of trigonometric functions 63
XI. Radio bearing conversion __ 110
XI1. Off-course correction tables. _ 113
XIII. Forms for solution of M orea tor and midlatitude flying 114
XIV. Table of correction for error in indicated free-air temperature
due to compression heat 114
XV. Conversion tables for metric and English linear measure... 115
APPENDIX Forms.
Figure 1. Ageton solution, line of position (W. D., A. A. F. Form
No. 21D) 116
2. Great circle computation, Ageton solution, course and
distance (W. D , A. A. F. Form No. 21Q) 117
3. Great circle computation, Ageton solution (Lat Lo of
intermediate pointx-1, x-2, etc.) (W. D., A. A. F.
Form No. 21R) 118
4. Factors for ground speed by timing (W. D., A. A. F.
FormTSfo. 21U) 119
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AIR NAVIGATION TABLES TM 1-208
This manual supersedes TM 1-208, 5 June 1942, including C /, if October 1942
Table I. NATURAL TRIGONOMETRIC FUNCTIONS'
Table of natural values of trigonometric functions. Table I contains the numerical values of the sines,
cosines, tangents, and cotangents of angles from 0 to 90 at intervals of 1'. In the case of an angle in the
range from 0 to 45, the number of degrees in the angle and the names of the functions are found at
the top of the page and the left-hand minute column applies; in the case of angles in the range from
45 to 90, the number of degrees in the angle and the names of the functions are found at the bottom
of the page and the right-hand minute column applies. Interpolation must be carried out without the
aid of difference columns or tables of proportional parts.
The following examples illustrate the method of using the tables.
Example 1. Find sin 6828'.
Solution. We first find the page at the bottom of which 68 appears and then find the row of the
68 block containing 28' in the right-hand minute column. In this row and in the column having sin
at its foot we find 020 to which we must prefix 0.93 to obtain sin 6828'=0.93020.
Example 2. Find sin 3838'27".
Solution. Using the tables and computing differences, we find the values exhibited in the following
form:
Hence
sin 3838'00"l0,,,l = 0.62433L. |
sin 3838'27"J27 60" =? f 23
sin 3839'00" I =0.62456 I
v 27 /27\
28-66' r HjT0>3= 10 (nearly).
Therefore
sin 3838'27"=0.62433+0.00010=0.62443. Ans.
Example 3. If cot 0=0.37806, find 6.
Solution. Using the tables and computing differences, we find the values exhibited in the following
form:
cot 6917'00"1_) =0.37820)
cot ? f 60=0.37806] ^[33
cot 6918'00" ) =0.37787
Hence
M-
j^j=> or x=(60) = 25" (nearly), and 0=6917'25". Ans.
Since cot 0 is positive in the third quadrant, we may also write an answer 180+6917'25" =
24917'25".
1 The following table of natural trigonometric functions and the explanation thereto have been prepared and copy-
righted by Lyman M. Kells, Willis F. Kern, and James R. Bland, who have supplied them to the Army Air Forces for
use in this publication. Neither the table nor any new feature embodied therein may be reproduced in any form with-
out the permission of the copyright owners.
M5S634O
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ARMY AIR FORCES
0 1
Table. I. Natural Trigonometric Functions
'
sin
tan
cot
cos
'
sin tan
cot
cos
0
. 00000
029
058
087
116
. 00000
029
058
087
116
1. 0000
000
000
000
000
60
0
.01745
. 01746
775
804
833
862
57. 290
56. 351
55. 442
54. 561
53. 709
. 99985
984
984
983
983
60
i
3437. 7
1718. 9
1145.9
859. 44
59
1
774
803
832
862
59
58
57
56
2
3
4
58
57
56
2
3
4
5
6
7
8
9
145
175
204
. 00233
262
145
175
204
. 00233
262
687. 55
572. 96
491. 11
429. 72
381. 97
000
000
000
000
000
55
54
53
52
51
5
6
7
8
9
891
920
949
.01978
. 02007
891
920
52. 882
52. 081
51. 303
982
982
55
54
53
52
51
949
.01978
. 02007
50. 549
49. 816
981
980
980
10
11
12
13
291
320
349
378
407
291
320
349
378
407
343. 77
312. 52
286. 48
264. 44
245. 55
1. 0000
. 99999
999
999
999
50
10
036
065
094
123
036
O66
095
124
153
49. 104
48. 412
47. 740
47. 085
46. 449
. 99979
979
978
977
50
49
48
47
46
11
12
13
49
48
47
46
14
14
152
977
15
16
17
18
19
436
465
.00495
524
553
436
465
. 00495
524
553
229. 18
214. 86
202. 22
190. 98
999
999
999
999
998
45
44
43
42
41
15
16
17
18
19
181
211
240
269
298
182
211
. 02240
269
298
45. 829
45. 226
44. 639
44. 066
43. 508
976
976
975
974
974
45
44
43
42
41
180. 93
20
21
22
23
24
582
611
640
669
698
582
611
640
669
698
171. 89
163. 70
156. 26
149. 47
143. 24
. 99998
998
998
998
998
40
39
38
37
36
20
. 02327
356
385
414
443
328
357
386
415
444
42. 964
42. 433
41. 916
41. 411
40. 917
. 99973
972
972
971
970
40
21
22
23
24
39
38
37
36
25
26
27
28
29
.00727
756
785
814
844
.00727
756
785
815
844
137. 51
132. 22
127. 32
122. 77
118. 54
997
997
997
997
996
35
34
33
32
31
25
26
27
28
29
472
501
530
560
589
473
. 02502
531
560
589
40. 436
39. 965
39. 506
39. 057
38. 618
969
969
968
967
966
35
34
33
32
31
30
31
32
33
873
902
931
960
. 00989
873
902
931
960
. 00989
114.59
110.89
107. 43
104. 17
101. 11
. 9999(3
996
996
995
995
30
30
. 02618
647
676
. 705
734
619
648
677
706
735
38. 188
37. 769
37. 358
36. 956
36. 563
. 99966
965
964
963
963
30
29
28
27
26
31
32
33
34
29
28
27
26
34
-
35
36
37
38
39
.01018
047
076
105
134
.01018
047
070
'105
135
98. 218
95. 489
92. 908
90. 463
88. 144
995
995
994
994
994
25
24
23
22
21
35
36
37
38
39
763
792
. 02821
850
879
. 02764
793
822
851
881
36. 178
35. 801
35. 431
35. 070
962
961
960
959
25
24
23
22
21
34. 715
959
40
41
42
43
44
164
193
222
.01251
280
164
193
222
251
. 01280
85. 940
83. 844
81. 847
79. 943
78. 126
. 99993
993
993
992
992
20
40
41
42
43
44
908
938
610
939
968
. 02997
. 03026
34. 368
34. 027
33. 694
33. 366
33. 045
. 99958
57
956
955
954
20
19
18
17
16
967
. 02996
. 03025
19
18
17
16
4i>
46
47
48
49
309
338
367
396
425
309
338
367
396
425
76. 390
74. 729
73. 139
71.615
70. 153
991
991
991
990
990
15
14
13
12
11
45
46
47
48
49
054
083
112
141
170
055
084
114
143
172
32. 730
32. 421
32. 118
31. 821
953
952
952
951
950
15
14
13
12
11
31. 528
50
454
483
.01513
542
571
455
484
.01513
542
571
68. 750
67. 402
66. 105
64. 858
63. 657
. 99989
989
989
988
988
10
9
50
199
228
. 03257
286
316
201
230
. 03259
288
317
31. 242
30. 960
30. 683
30. 412
30. 145
. 99949
948
947
946
945
10
51
52
53
54
51
52
53
54
9
8
7
6
8
7
6
55
56
57
58
59
60
600
629
658
687
716
.01745
600
629
658
687
716
.01746
62. 499
61.383
60. 306
59. 266
58. 261
57.290
987
987
986
986
085
. 99985
5
4
3
2
1
0
55
56
57
58
59
60
345
374
403
432
461
. 03490
346
376
405
434
463
. 03492
29. 882
29. 624
29. 371
29. 122
28. 877
28. 636
944
943
942
941
940
. 99939
5
4
3
2
1
0
cos
cot
tan
sin
/
C08
cot
tan
sin
/
89 88
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AIR NAVIGATION TABLES
Table /, Natural Trigonometric Functions Continued
2 3
/
sin
tan
cot
cos
/
sin
tan
cot
cos
0
. 03490
519
548
577
606
. 03492
521
550
579
609
28. 636
.399
28. 166
27.937
.712
.99939
938
937
936
935
60
0
. 05234
263
292
321
350
.05241
270
299
328
357
19. 081
18. 976
.871
.768
.666
. 99863
861
860
858
857
60
i
59
58
57
56
1
59
58
57
56
2
3
4
2
3
4
5
6
635
664
693
723
. 03752
638
.490
.271
27.057
26. 845
.637
934
933
932
931
930
55
54
53
52
51
5
379
408
437
466
. 05495
387
416
445
474
. 05503
.564
. 464
.366
.268
. 171
855
854
852
851
849
55
54
53
52
51
7
8
9
667
696
. 03725
754
6
7
8
9
10
11
12
13
781
810
839
868
897
783
812
842
871
900
.432
.230
26. 031
25. 835
. 99929
927
926
925
924
50
49
48
47
46
10
11
12
524
553
582
611
640
533
562
591
620
649
18. 075
17. 980
. 99847
846
844
842
841
50
14
.642
13
14
.886
.793
.702
49
48
47
46
15
16
926
955
. 03984
. 04013
042
929
958
. 03987
.04016
046
.452
.264
25. 080
923
922
921
919
918
45
44
43
42
41
15
16
17
18
19
669
698
. 05727
756
785
678
708
737
. 05766
795
.611
.521
.431
.343
839
838
836
834
833
45
44
43
42
41
17
18
19
24.898
.719
. 256
20
071
100
075
104
133
162
191
.542
.368
. 196
24. 026
23. 859
. 99917
916
915
913
912
40
20
21
22
23
24
814
844
873
902
931
824
854
883
912
941
. 169
17. 084
16. 999
.915
. 99831
829
827
826
824
40
21
22
23
24
129
159
188
39
38
37
36
.832
39
38
37
36
25
26
27
28
29
217
246
. 04275
304
333
220
. 04250
279
308
337
.695
.532
.372
.214
23. 058
911
910
909
907
906
35
34
33
32
31
25
26
27
28
29
960
. 05989
.06018
047
970
. 05999
. 06029
058
087
.750
.668
.587
16. 507
.428
822
821
819
817
815
35
34
33
32
31
076
30
362
391
420
449
478
366
395
424
454
. 04483
22. 904
.752
.602
.454
. 99905
904
902
901
900
30
30
105
134
163
192
221
116
145
175
204
233
.350
.272
.195
.119
16. 043
. 99813
812
810
808
806
30
31
32
33
34
.308
29
28
27
26
31
32
33
34
29
28
27
26
35
36
37
38
39
. 04507
536
565
594
623
512
541
570
599
628
. 164
22. 022
21.881
.743
.606
898
897
896
894
893
25
24
23
22
21
35
36
37
38
39
. 06250
279
308
337
366
262
. 06291
321
350
379
15. 969
804
803
801
799
25
24
23
22
21
.895
.821
.748
.676
797
40
653
682
.04711
740
769
658
687
. 04716
745
774
.470
.337
.205
21. 075
20. 946
. 99892
890
889
888
886
20
40
395
424
453
. 06482
511
408
438
467
496
. 06525
.605
.534
15. 464
.394
.325
. 99795
793
792
790
20
41
42
43
19
18
17
16
41
42
43
44
19
18
17
16
44
788
45
46
47
48
49
798
827
856
885
914
803
833
862
891
920
.819
.693
.569
.446
.325
885
883
882
881
879
15
14
13
12
11
45
46
47
48
49
540
569
598
627
656
554
584
613
642
.257
.189
.122
15. 056
14. 990
786
784
782
780
,778
15
14
13
12
11
671
50
943
. 04972
.05001
030
. 059
949
. 04978
. 05007
037
066
.206
20. 087
19. 970
.855
.740
. 99878
876
875
873
872
10
50
685
. 06714
743
773
700
730
.06759
788
817
.924
.860
.795
.732
.669
. 99776
774
772
770
768
10
51
52
53
54
9
8
7
6
51
62
53
54
802
9
8
7
6
55
66
57
58
59
60
088
117
146
175
205
. 05234
095
124
153
182
212
. 05241
.627
.516
.405
.296
.188
19. 081
870
869
867
866
864
.99863
5
4
3
2
1
0
55
56
57
58
59
60
831
860
889
918
947
.06976
847
876
905
934
963
. 06993
.606
766
784
762
760
758
.99756
5
4
3
2
1
0
. J i l
.482
.421
.361
14. 301
cos
cot
tan
sin
/
cos
cot
tan
sin
/
87 86
Gen
erat
ed o
n 20
13-1
0-17
19:
33 G
MT
/ h
ttp:
//hdl
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dle.
net/
2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
digi
tized
/ h
ttp:
//ww
w.h
athi
trus
t.or
g/ac
cess
_use
#pd
-goo
gle
-
ARMY AIR FORCES
Table I. Natural Trigonometric Functions Continued
4 5
'
sin
tan
cot
cos
/
sin
tan
cot
cos
0
. OB976
.07005
034
063
092
. 06993
. 07022
051
080
110
14. 301
. 99756
754
752
750
748
60
0
1
.08716
745
774
803
831
. 08749
778
807
837
866
11.430
.392
.354
.316
.279
.99619
617
614
612
609
60
i
.241
. 182
.124
.065
59
58
57
56
59
58
57
56
2
3
2
3
4
4
5
6
7
8
9
121
150
179
208
237
139
168
197
227
. 07256
14. 008
13.951
.894
.838
.782
746
744
742
740
738
55
54
53
52
51
5
6
7
8
9
860
889
918
947
. 08976
895
925
954
. 08983
.09013
.242
.205
.168
.132
.095
607
604
602
599
596
55
54
53
52
51
10
. 07266
295
324
353
382
285
314
344
373
402
.727
.672
.617
.563
13. 510
. 99736
734
731
729
50
10
. 09005
034
063
092
121
042
071
101
130
159
.059
11. 024
10. 988
.953
. 99594
591
588
586
583
50
11
12
13
14
49
48
47
46
11
49
48
47
46
727
12
13
14
.918
15
16
17
18
19
411
440
469
. 07498
527
431
461
490
. 07519
548
.457
.404
.352
.300
.248
725
723
721
719
716
45
44
43
42
41
15
16
17
18
19
150
179
208
. 09237
266
189
218
. 09247
277
306
.883
.848
.814
.780
.746
580
578
575
572
570
45
44
43
42
41
20
556
585
614
643
672
578
607
636
665
695
.197
. 146
.096
13.046
12. 996
. 99714
712
710
708
705
40
20
295
324
353
382
411
335
365
. 712
.678
10. 645
.612
.579
. 99567
564
562
559
556
40
21
22
23
24
39
38
37
36
21
22
23
24
394
423
453
39
38
37
36
25
26
27
28
29
701
. 07730
759
724
. 07753
782
812
841
.947
.898
.850
.801
.754
703
701
699
696
694
35
34
33
32
31
25
26
27
28
29
440
. 09469
498
527
556
. 09482
511
541
570
600
.546
.514
.481
.449
.417
553
651
548
545
542
35
34
33
32
31
788
817
30
846
875
904
933
962
870
899
929
958
. 07987
. 706
.659
12. 612
.566
.520
. 99692
689
687
685
683
30
30
585
614
642
671
700
629
658
688
. 09717
746
.385
.354
10. 322
.291
.260
. 99540
537
534
531
528
30
31
32
33
34
29
31
32
33
34
29
28
27
26
28
27
26
35
36
37
38
39
.07991
. 08020
049
078
107
.08017
046
075
104
134
.474
.429
.384
12. 339
.295
680
678
676
673
671
25
24
23
22
21
35
36
37
38
39
. 09729
758
787
816
845
776
805
834
864
893
.229
.199
.168
.138
. 108
526
523
520
517
514
25
24
23
22
21
40
136
165
194
223
163
192
.251
.207
.163
.120
.077
. 99668
666
664
661
659
20
40
874
903
932
961
.09990
923
.078
.048
10.019
9. 9893
.9601
.99511
508
506
503
500
20
41
42
43
44
. 08252
221
.08251
280
19
18
17
16
41
42
43
44
952
. 09981
.10011
040
19
18
17
16
45
46
47
48
49
281
310
339
368
397
309
339
368
397
427
12. 035
11.992
.950
.909
.867
657
654
652
649
647
15
14
13
45
46
47
48
49
. 10019
048
077
106
135
069
099
128
.9310
.9021
.8734
.8448
.8164
497
494
491
15
14
13
12
11
12
11
158
187
488
485
50
426
455
. 08484
513
542
456
485
. 08514
544
573
.826
.785
.745
.705
11.664
. 99644
642
639
637
635
10
50
51
52
53
164
192
221
. 10250
279
216
. 10246
275
305
334
.7882
.7601
9. 7322
.7044
.6768
. 99482
479
476
473
470
10
9
51
52
53
54
9
8
7
8
7
6
6
54
55
56
57
58
59
60
571
600
629
658
687
. 08716
602
632
661
690
720
. 08749
.625
.585
.546
.507
.468
11. 430
632
630
627
625
622
.99619
b
4
3
2
1
0
55
56
57
58
59
60
308
337
366
395
424
. 10453
363
393
422
452
481
. 10510
. 6493
.6220
.5949
.5679
.5411
9. 5144
467
464
461
458
455
. 99452
5
4
3
2
1
0
cos
cot
tan
sin
/
cos
cot
tan
sin
83
84
Gen
erat
ed o
n 20
13-1
0-18
05:
33 G
MT
/ h
ttp:
//hdl
.han
dle.
net/
2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
digi
tized
/ h
ttp:
//ww
w.h
athi
trus
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g/ac
cess
_use
#pd
-goo
gle
-
AIR NAVIGATION TABLES
Table I. Natural Trigonometric Functions Continued
6 7
/
sin
tan
cot
cos
/
sin
tan
cot
cos
0
. 10453
482
511
540
569
.10510
540
9.5144
. 99452
449
446
443
440
60
0
. 12187
216
245
274
302
. 12278
308
338
367
397
8. 1443
. 1248
. 1054
.0860
. 99255
251
248
244
240
60
i
.4878
.4614
.4352
.4090
59
58
57
56
1
2
3
59
58
57
56
2
3
569
599
628
4
4
.0667
5
6
7
8
9
597
626
655
684
. 10713
657
687
716
. 10746
775
.3831
.3572
.3315
.3060
. 2806
437
434
431
428
55
54
53
52
51
5
6
7
8
9
331
426
456
485
. 12515
544
.0476
.0285
8.0095
7. 9906
.9718
237
233
230
55
54
53
52
51
424
360
389
418
. 12447
226
222
10
742
771
800
829
805
834
863
893
922
9. 2553
.2302
.2052
. 1803
. 1555
.99421
418
415
412
409
50
10
476
504
533
562
591
574
603
633
662
692
.9530
.9344
.9158
.8973
.8789
. 99219
215
211
208
50
11
49
48
47
46
11
12
13
14
49
48
47
46
12
13
14
858
204
15
16
17
18
19
887
916
945
. 10973
. 11002
952
. 10981
.11011
040
070
. 1309
. 1065
. 0821
.0579
.0338
406
402
399
396
393
45
44
43
42
41
15
16
17
18
19
620
649
678
. 12706
735
722
. 12751
781
810
840
. 8606
7. 8424
.8243
. 8062
.7882
200
197
193
189
45
44
43
42
41
186
20
031
099
128
158
187
217
9. 0098
8. 9860
.9623
.9387
.9152
. 99390
386
383
380
377
40
20
764
793
822
851
880
869
899
929
958
.7704
.7525
.7348
.7171
.6996
.99182
178
175
171
167
40
21
22
23
24
060
39
38
37
36
21
22
23
24
39
38
37
36
089
118
147
. 12988
25
26
27
28
29
176
205
234
. 11263
291
. 11246
276
305
335
.8919
.8686
.8455
.8225
.7996
374
370
35
34
33
32
31
25
26
27
28
29
908
937
966
. 12995
. 13024
. 13017
047
076
106
136
7. 6821
.6647
.6473
.6301
.6129
163
160
156
152
148
35
34
33
32
31
364
367
364
360
30
31
32
33
320
349
378
407
436
394
423
452
. 11482
511
. 7769
8. 7542
.7317
.7093
.6870
. 99357
354
351
347
344
30
30
053
081
110
139
165
195
224
. 13254
.5958
.5787
.5618
.5449
.99144
141
137
133
129
30
29
28
27
26
31
32
33
34
29
28
27
34
168
284
7. 5281
26
35
36
37
38
39
465
494
. 11523
552
541
570
600
629
659
.6648
.6427
.6208
.5989
341
337
334
331
327
25
24
23
22
21
35
36
37
38
39
197
. 13226
254
283
312
313
343
372
402
432
. 5113
.4947
.4781
.4615
.4451
125
122
118
114
110
25
24
23
22
21
580
.5772
40
609
638
667
696
725
688
. 11718
747
777
806
. 5555
8. 5340
.5126
.4913
.4701
. 99324
320
317
314
310
20
19
40
341
370
399
427
. 13456
461
. 13491
521
550
580
.4287
.4124
.3962
7.3800
.3639
. 99106
102
098
"094
091
20
41
42
43
44
18
17
16
41
42
43
44
19
18
17
16
45
46
47
48
49
. 11754
783
812
840
869
836
865
895
924
954
.4490
.4280
.4071
.3863
.3656
307
303
300
297
293
15
14
13
12
11
45
46
47
48
49
485
514
543
572
600
609
639
669
698
. 13728
.3479
.3319
. 3160
.3002
. 2844
087
083
079
075
071
15
14
13
12
11
50
51
52
53
54
898
927
. 956
.11985
. 12014
.11983
. 12013
042
072
101
.3450
8. 3245
.3041
.2838
.2636
. 99290
286
283
279
10
9
50
629
658
. 13687
716
744
758
787
817
846
876
.2687
7. 2531
.2375
.2220
.2066
.99067
063
059
055
051
10
276
8
7
6
51
52
53
54
9
8
7
6
55
56
57
58
59
60
043
071
100
129
158
. 12187
131
160
190
219
249
. 12278
.2434
.2234
.2035
. 1837
. 1640
8. 1443
272
269
265
262
258
.99255
5
4
3
2
1
0
55
56
57
58
59
60
773
802
831
860
889
.13917
906
935
965
. 13995
. 14024
. 14054
. 1912
.1759
. 1607
. 1455
. 1304
7. 1154
047
043
039
035
031
.99027
5
4
3
2
1
0
cos
cot
tan
sin
/
cos
cot
tan
sin
/
83 82
Gen
erat
ed o
n 20
13-1
0-18
05:
33 G
MT
/ h
ttp:
//hdl
.han
dle.
net/
2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
digi
tized
/ h
ttp:
//ww
w.h
athi
trus
t.or
g/ac
cess
_use
#pd
-goo
gle
-
ARMY AIR FORCES
Table I. Natural Trigonometric Functions Continued
8 9
/
sin
tan
cot
cos
/
sin
tan
cot
cos
0
.13917
946
. 13975
. 14004
033
. 14054
084
113
143
173
7.1154
.1004
.0855
.0706
.0558
. 99027
023
019
015
Oil
60
0
. 15643
672
701
730
. 15838
868
898
928
958
6.3138
.3019
.2901
.2783
.2666
. 98769
764
760
755
751
60
i
59
58
57
56
1
2
3
59
58
57
56
2
3
4
4
758
5
061
690
119
148
177
202
232
262
. 14291
321
.0410
.0264
7.0117
6. 9972
.9827
006
. 99002
. 98998
994
990
55
54
53
52
51
5
6
7
8
9
787
. 15816
845
873
902
. 15988
.16017
047
077
107
. 2549
.2432
.2316
. 2200
6. 2085
746
741
737
732
728
55
54
53
52
51
6
7
8
9
10
205
. 14234
263
292
351
381
410
440
470
. 9682
.9538
.9395
.9252
.9110
986
982
978
973
969
50
49
10
11
931
959
. 15988
. 16017
046
137
167
196
226
. 1970
. 1856
.1742
. 1628
-. 1515
. 98723
718
714
709
704
50
49
11
12
48
47
46
12
13
14
48
47
46
13
14
320
. 16256
15
16
17
18
19
349
378
499
. 14529
559
.8969
.8828
6. 8687
.8548
.8408
965
961
. 98957
953
948
45
44
43
42
41
15
16
17
18
19
074
103
132
160
286
316
346
376
405
. 1402
. 1290
. 1178
6. 1066
.0955
700
695
690
686
681
45
44
43
42
41
407
436
464
588
618
189
20
21
22
23
24
. 14493
522
551
580
608
648
678
707
737
. 14767
.8269
.8131
.7994
.7856
.7720
944
940
936
931
927
40
20
21
22
23
24
218
246
. 16275
304
333
435
465
. 16495
525
555
.0844
.0734
.0624
.0514
.0405
. 98670
671
667
662
657
40
39
38
37
36
39
38
37
36
25
26
27
28
29
637
666
- 695
. 14723
752
796
826
856
886
915
6. 7584
.7448
.7313
.7179
.7045
. 98923
919
914
910
906
35
34
33
32
31
25
26
27
28
29
361
390
585
615
645
674
. 0296
.0188
6. 0080
5. 9972
.9865
652
648
643
638
633
35
34
33
32
31
419
447
476
704
30
31
32
33
34
781
810
838
867
896
945
. 14975
. 15005
034
064
.6912
.6779
.6646
.6514
6. 6383
902
897
893
889
30
30
31
32
33
34
505
. 16533
562
591
620
. 16734
764
794
824
854
.9758
.9651
.9545
.9439
.9333
. 98629
624
619
614
609
30
29
28
27
26
. 98884
29
28
27
26
35
36
37
38
39
925
954
. 14982
.15011
040
094
124
153
183
213
.6252
.6122
.5992
.5863
.5734
880
876
871
867
863
25
24
23
22
21
35
36
37
38
39
648
677
706
734
. 16763
884
914
944
. 16974
. 17004
. 9228
5. 9124
.9019
.8915
.8811
604
600
595
590
585
25
24
23
22
21
40
41
42
43
069
097
126
155
243
. 15272
302
332
362
. 5606
.5478
.5350
6. 5223
858
854
849
. 98845
841
20
40
41
42
43
44
792
820
849
878
906
033
063
093
123
153
.8708
.8605
.8502
.8400
5. 8298
. 98580
575
570
565
561
20
44
184
.5097
19
18
17
16
19
18
17
16
45
46
47
48
49
. 15212
241
270
299
327
391
421
451
481
511
.4971
.4846
.4721
.4596
.4472
836
832
827
823
15
14
13
12
11
45
46
47
48
49
935
964
. 16992
. 17021
050
183
. 17213
243
273
303
. 8197
.8095
.7994
.7894
.7794
556
551
546
541
536
15
14
13
12
11
818
50
356
385
. 15414
442
471
. 15540
570
600
630
660
.4348
.4225
6. 4103
.3980
.3859
814
809
. 98805
800
796
10
50
078
107
136
164
. 17193
333
363
393
. 17423
453
.7694
. 7594
5. 7495
.7396
.7297
. 98531
526
521
516
511
10
51
52
53
54
9
8
7
6
51
52
53
9
8
7
6
54
55
56
57
58
59
60
500
529
557
586
615
. 15643
689
719
749
779
809
. 15838
.3737
.3617
.3496
.3376
.3257
6.3138
791
787
782
778
773
. 98769
5
4
3
2
1
0
55
56
57
58
59
60
222
250
279
308
336
. 17365
483
513
543
573
603
. 17633
.7199
.7101
.7004
.6906
.6809
5.6713
506
501
496
491
486
. 98481
5
4
3
2
1
0
cos
cot
tan
sin
/
cos
cot
tan
sin
/
81 80
Gen
erat
ed o
n 20
13-1
0-18
05:
33 G
MT
/ h
ttp:
//hdl
.han
dle.
net/
2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
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tized
/ h
ttp:
//ww
w.h
athi
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t.or
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cess
_use
#pd
-goo
gle
-
AIR NAVIGATION TABLES
Table I. Natural Trigonometric Functions Continued
10 11
/
sin
tan
cot
cos
1
sin
tan
cot
cos
0
. 17365
393
422
451
479
. 17633
663
693
723
753
5.6713
.6617
.6521
.6425
. 6329
.98481
476
471
466
461
60
0
.19081
109
138
167
195
. 19438
468
498
529
559
5. 1446
. 1366
. 1286
. 1207
. 1128
.98163
157
152
146
140
60
i
59
1
59
58
57
56
2
3
58
57
56
2
3
4
4
5
6
7
8
9
508
537
. 17565
594
623
783
. 17813
843
873
903
. 6234
.6140
. 6045
.5951
. 5857
455
450
445
440
435
55
54
53
52
51
5
6
7
224
252
281
. 19309
338
589
619
649
680
. 19710
. 1049
.0970
.0892
.0814
5. 0736
135
129
124
118
.98112
55
54
53
52
51
8
9
10
651
680
708
737
766
933
963
. 17993
.18023
053
5. 5764
.5671
.5578
.5485
.5393
. 98430
425
420
414
409
50
10
366
395
423
452
740
770
801
831
861
. 0658
.0581
.0504
.0427
. 0350
107
101
096
090
084
50
11
12
13
14
49
48
47
46
11
12
13
49
48
47
46
14
481
15
16
17
18
19
. 17794
823
852
880
909
083
113
143
173
203
. 5301
.5209
.5118
.5026
.4936
404
399
394
389
383
45
44
43
42
41
15
16
17
18
509
. 19538
566
595
623
891
921
952
. 19982
.20012
.0273
.0197
.0121
5. 0045
4. 9969
079
073
067
061
. 98056
45
44
19
43
42
41
20
937
966
. 17995
. 18023
052
233
. 18263
293
323
353
5. 4845
.4755
.4665
.4575
.4486
. 98378
373
368
362
357
40
39
38
37
36
20
21
22
23
652
680
709
737
. 19766
042
073
103
133
. 9894
.9819
.9744
.9669
.9594
050
044
039
033
027
40
21
22
23
24
24
164
39
38
37
36
25
26
27
28
29
081
109
138
166
195
384
414
444
474
. 18504
.4397
.4308
.4219
.4131
.4043
352
347
341
336
331
35
34
33
32
31
25
26
27
28
29
794
823
851
880
908
194
. 20224
254
285
315
. 9520
.9446
4.9372
.9298
.9225
021
016
010
35
34
33
32
31
. 98004
. 97998
30
224
252
. 18281
309
338
534
564
594
624
654
5. 3955
.3868
.3781
.3694
.3607
. 98325
320
315
310
304
30
30
937
965
. 19994
. 20022
051
345
376
406
436
.9152
.9078
.9006
.8933
.8860
992
987
'981
975
969
30
31
29
28
27
26
31
32
33
34
29
28
27
26
32
33
34
. 20466
35
36
37
38
367
395
424
452
684
714
. 18745
775
805
.3521
.3435
.3349
.3263
.3178
299
294
288
283
277
25
24
23
22
21
35
36
37
38
39
079
108
136
165
193
497
527
557
588
618
4. 8788
.8716
.8644
.8573
.8501
963
958
. 97952
946
940
25
24
23
22
21
39
481
\
40
. 18509
538
567
595
624
835
865
895
925
5. 3093
.3008
.2924
.2839
.2755
. 98272
267
261
256
250
20
40
222
250
. 20279
307
336
648
679
709
. 20739
770
.8430
.8359
.8288
.8218
4. 8147
934
928
922
916
. 97910
20
41
42
43
44
19
41
42
43
19
18
17
16
955
18
17
16
44
45
46
652
681
710
738
. 18767
. 18986
. 19016
046
076
106
.2672
.2588
.2505
.2422
.2339
245
240
234
229
223
15
14
13
12
11
45
46
47
48
49
364
393
421
450
800
830
861
891
921
.8077
.8007
.7937
.7867
.7798
905
899
893
887
881
15
14
13
12
11
47
48
49
478
50
795
824
852
881
910
136
166
197
. 19227
257
5. 2257
.2174
.2092
.2011
. 1929
.98218
212
207
201
196
10
50
507
. 20535
563
592
620
952
. 20982
.21013
043
073
.7729
.7659
4.7591
.7522
.7453
875
869
. 97863
857
851
10
51
52
53
54
9
51
52
53
54
9
8
7
6
8
7
6
55
56
57
58
59
60
938
967
. 18995
. 19024
052
.19081
287
317
347
378
408
. 19438
. 1848
. 1767
. . 1686
. 1606
. 1526
5. 1446
190
185
179
174
168
.98163
5
4
3
2
1
0
55
56
57
58
59
60
649
677
706
734
763
.20791
104
134
164
195
225
. 21256
.7385
.7317
.7249
.7181
. 7114
4. 7046
845
839
833
827
821
.97815
5
4
3
2
1
0
cos
cot
tan
sin
/
cos
cot
tan
sin
/
79 78
Gen
erat
ed o
n 20
13-1
0-18
05:
33 G
MT
/ h
ttp:
//hdl
.han
dle.
net/
2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
digi
tized
/ h
ttp:
//ww
w.h
athi
trus
t.or
g/ac
cess
_use
#pd
-goo
gle
-
ARMY AIR FORCES
Table I. Natural Trigonometric Functions Continued
12 13
/
sin
tan
cot
cos
sin
tan
cot
cos
0
. 20791
820
848
877
905
.21256
286
316
347
377
4. 7046
4. 6979
912
845
779
.97815
809
803
797
7S1
60
0
.22495
523
552
580
608
. 23087
117
148
179
209
4.3315
257
200
143
086
. 97437
430
424
417
60
i
59
58
57
56
1
2
3
59
58
57
56
2
3
4
4
411
5
6
933
962
. 20990
.21019
047
408
438
469
. 21499
529
712
646
580
4. 6514
448
784
778
772
766
760
55
54
53
52
5
6
7
8
9
637
665
693
. 22722
750
240
271
23301
332
363
4. 3029
4. 2972
916
859
803
404
398
391
384
378
55
54
53
52
51
7
8
9
51
10
11
076
104
132
161
189
560
590
621
651
682
382
317
252
187
122
. 97754
748
742
735
729
50
10
778
807
835
863
892
393
424
455
485
516
747
691
635
580
4. 2524
. 97371
365
358
351
345
50
49
11
49
48
47
46
12
13
48
47
46
12
13
14
14
15
16
17
18
19
218
. 21246
275
303
331
712
. 21743
773
804
834
4. 6057
4. 5993
928
864
800
723
717
711
705
45
44
43
42
41
15
16
17
18
19
920
948
. 22977
.23005
033
. 23547
578
608
639
670
468
413
358
303
248
338
331
325
318
311
45
44
43
42
41
698
20
360
388
417
445
474
864
895
925
956
.21986
736
673
609
4.5546
483
. 97692
686
680
673
667
40
20
21
062
090
118
700
731
. 23762
793
823
193
139
084
4. 2030
4. 1976
. 97304
298
291
284
278
40
39
38
37
36
21
22
23
24
39
38
37
36
22
23
24
146
175
25
26
27
28
29
. 21502
530
559
587
616
.22017
047
078
108
139
420
357
294
232
169
661
655
648
642
636
35
34
33
32
31
25
26
27
28
29
203
231
. 23260
288
316
854
885
916
946
. 23977
922
868
814
760
706
271
264
257
251
244
35
34
33
32
31
30
644
672
701
729
. 21758
169
200
231
. 22261
292
107
4. 5045
4. 4983
922
860
. 97630
623
617
611
604
30
30
345
373
. 24008
039
069
100
131
653
600
547
4. 1493
441
. 97237
230
223
217
210
30
31
32
33
34
29
28
27
26
31
32
33
34
401
429
458
29
28
27
26
35
36
37
38
39
786
814
843
871
899
322
353
383
414
444
799
- 737
676
615
555
598
592
585
579
573
25
24
23
22
21
35
36
37
38
39
. 23486
514
542
571
599
162
193
388
335
282
230
203
25
24
23
22
21
223
. 24254
285
178
196
189
182
176
40
928
956
. 21985
.22013
041
475
. 22505
536
567
597
4. 4494
434
373
313
253
. 97566
560
553
547
541
20
40
627
656
684
712
. 23740
316
347
377
126
074
4. 1022
4. 0970
918
. 97169
162
155
148
141
20
19
18
17
41
42
43
44
19
18
17
16
41
42
43
408
439
44
16
45
46
47
48
49
070
098
126
155
183
628
658
689
719
. 22750
194
134
075
4.4015
4. 3956
534
528
521
515
508
15
14
13
12
11
45
46
47
769
797
825
853
. 24470
501
532
562
867
815
764
713
662
134
127
120
15
14
13
12
11
48
49
882
593
113
106
50
212
240
. 22268
297
325
781
811
842
872
903
897
838
779
721
662
. 97502
496
489
483
476
10
50
910
938
966
. 23995
. 24023
624
655
611
560
4.0509
459
408
. 97100
093
086
079
072
10
51
52
53
9
8
7
6
51
52
53
54
. 24686
717
747
9
8
7
6
54
55
56
57
58
59
60
353
382
410
438
467
. 22495
934
964
. 22995
. 23026
056
. 23087
604
546
488
430
372
4.3315
470
463
457
450
444
. 97437
5
4
3
2
1
0
55
56
57
58
59
60
051
079
108
136
164
.24192
778
809
840
871
902
.24933
358
308
257
207
158
4.0108
065
058
051
044
037
. 97030
5
4
3
2
1
0
cos
cot
tan
sin
cos
cot
tan
sin
/
77 76
Gen
erat
ed o
n 20
13-1
0-18
05:
34 G
MT
/ h
ttp:
//hdl
.han
dle.
net/
2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
digi
tized
/ h
ttp:
//ww
w.h
athi
trus
t.or
g/ac
cess
_use
#pd
-goo
gle
-
AIR NAVIGATION TABLES
Table I. Natural Trigonometric Functions Continued
14 15
'
sin
tan
cot
cos
7
sin
tan
cot
cos
0
.24192
220
249
277
305
. 24933
964
. 24995
. 25026
056
4. 0108
058
4.0009
3. 9959
910
. 97030
023
015
008
.97001
60
0
. 25882
910
933
966
. 25994
. 26795
826
857
888
'920
3.7321
277
234
191
148
. 96593
585
578
570
562
60
59
i
59
58
57
56
1
2
3
4
2
3
58
57
56
4
5
6
7
8
9
333
362
390
418
087
118
149
180
211
861
812
763
714
665
. 96994
987
980
973
966
55
54
53
52
51
5
6
7
8
9
.26022
050
079
107
135
951
. 26982
.27013
044
076
105
062
3.7019
3. 6976
933
555
547
540
532
524
55
54
53
52
51
. 24446
10
474
503
531
1 559
587
242
. 25273
304
335
366
617
568
3. 9520
471
423
959
952
945
. 96937
930
50
10
163
191
219
. 26247
275
107
138
169
201
232
891
848
806
764
722
. 96517
509
502
494
486
50
Ml
12
13
14
49
48
47
46
11
12
13
49
14
48
47
46
15
16
17
18
19
615
644
672
700
. 24728
397
428
459
. 25490
521
375
327
279
232
184
923
916
909
902
894
45
44
43
42
41
15
16
17
18
19
303
331
359
. 27263
294
326
357
388
680
3. 6638
596
554
512
479
471
463
456
448
45
44
43
42
41
387
415
20
756
784
813
841
869
552
583
614
645
676
136
089
3. 9042
3.8995
947
887
.96880
873
866
858
40
20
21
22
23
24
443
.26471
500
528
419
451
. 27482
513
545
470
429
387
346
3. 6305
. 96440
433
425
417
410
40
21
22
23
24
39
38
37
36
556
39
38
37
36
25
26
27
28
29
897
925
954
. 24982
. 25010
707
. 25738
769
800
831
900
854
807
760
714
851
35
34
33
32
31
25
584
612
640
668
696
576
607
'638
670
701
264
222
181
140
100
402
394
386
379
371
35
34
33
32
31
844
837
829
. 96822
26
27
28
29
30
31
32
33
34
038
066
094
122
151
862
893
924
955
3. 8667
621
575
528
482
815
807
800
793
786
30
30
. 26724
752
780
808
836
. 27732
764
795
826
858
059
3.6018
3. 6978
937
. 897
. 96363
355
347
340
332
30
29
28
27
26
29
28
31
32
33
34
. 25986
27
26
35
36
37
38
39
179
207
. 25235
263
291
.26017
048
079
110
141
436
391
3. 8345
299
254
778
771
. 96764
756
749
25
24
23
35
36
37
38
39
864
892
920
948
. 26976
889
921
952
.27983
.28015
856
816
776
736
324
316
308
301
293
25
24
23
22
21
22
21
696
40
41
42
43
320
348
376
172
203
235
. 26266
297
208
163
118
073
3. 8028
742
734
727
719
20
19
18
17
16
40
.27004
032
060
088
116
046
077
109
140
172
3. 5656
616
576
536
497
. 96285
277
269
261
253
20
19
18
17
16
44
404
. 25432
712
41
42
43
44
45
46
47
48
49
460
488
516
545
573
328
359
390
421
452
3. 7983
938
893
848
804
. 96705
697
690
682
675
15
14
13
12
11
45
46
47
144
172
200
228
256
203
. 28234
266
297
329
457
418
379
3. 5339
300
246
238
230
222
214
15
14
13
12
11
48
49
50
51
52
53
54
601
629
. 25657
685
713
483
515
. 26546
577
608
760
715
a 7671
627
583
667
660
653
. 96645
638
10
50
. 27284
312
340
368
396
360
391
423
261
222
183
144
105
. 96206
198
190
182
174
10
9
8
7
6
51
52
53
54
.28454
486
9
8
7
6
55
56
57
58
59
60
741
769
798
826
854
.25882
639
670
701
733
539
495
451
408
364
3. 7321
630
623
615
608
600
. 96593
5
4
3
2
1
0
55
56
57
58
59
60
424
452
480
508
536
.27564
517
549
580
612
643
. 28675
067
3. 5028
3. 4989
951
912
3. 4874
166
158
150
142
134
.96126
5
4
3
2
1
0
764
. 26795
cos
cot
tan
sin
cos
cot
tan
sin
/
75 74
Gen
erat
ed o
n 20
13-1
0-18
05:
34 G
MT
/ h
ttp:
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ttp:
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w.h
athi
trus
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cess
_use
#pd
-goo
gle
-
ARMY AIR FORCES
Table I. Natural Trigonometric Functions Continued
16 17
*
sin
tan
cot
cos
/
sin
tan
cot
cos
0
. 27564
592
620
648
676
. 28675
706
738
769
801
3. 4874
836
798
760
722
.96126
118
110
102
094
60
0
. 29237
265
293
321
348
. 30573
605
637
669
700
3. 2709
675
641
607
573
. 95630
622
613
605
596
60.
i
59
58
57
56
1
59
58
57
56
2
3
4
2
3
4
5
6
7
8
9
704
731
. 27759
787
815
832
864
895
927
958
684
646
608
a 4570
533
086
078
. 96070
062
054
55
54
53
52
51
5
6
7
8
9
376
404
432
460
732
539
506
3. 2472
438
405
588
579
571
562
554
55
764
. 30796
54
53
52
51
. 29487
828
860
10
11
12
843
871
899
927
955
. 28990
. 29021
053
084
116
495
458
420
383
346
046
037
029
021
013
50
10
515
543
571
599
626
891
923
955
. 30987
.31019
371
338
305
272
3. 2238
. 95545
536
528
519
511
50
13
49
48
47
46
11
12
13
14
49
48
47
46
14
15
16
17
18
19
. 27983
.28011
039
067
095
147
179
210
. 29242
274
a 4308
271
234
197
160
. 96005
. 95997
989
981
972
45
44
43
42
41
15
16
17
18
19
654
682
710
. 29737
765
051
083
115
147
178
205
172
139
106
073
502
493
485
476
467
45
44
43
42
41
20
123
150
178
206
305
337
124
087
050
3. 4014
3. 3977
964
956
948
940
931
40
20
793
821
849
876
904
210
242
. 31274
306
041
3. 2008
3. 1975
943
. 95459
450
441
433
424
40
21
22
23
24
368
400
432
39
38
37
36
21
22
23
39
38
37
36
. 28234
24
338
910
25
26
27
28
29
262
290
318
346
. 29463
495
526
558
590
941
904
868
832
796
. 95923
915
907
898
890
35
34
33
32
31
25
26
27
28
29
932
960
.29987
.30015
043
370
402
434
466
. 31498
878
845
813
780
3. 1748
415
407
398
389
380
35
34
33
32
31
374
30
31
32
33
34
402
429
457
.28485
513
621
653
759
723
687
3. 3652
616
882
874
865
. 95857
849
30
30
31
32
33
34
071
098
126
154
182
530
562
594
626
658
716
684
652
620
. 95372
363
354
345
337
30
685
. 29716
748
29
28
27
26
588
29
28
27
26
35
36
37
38
39
541
569
597
625
652
780
811
843
875
906
580
544
509
473
438
841
832
25
24
23
22
21
35
36
37
38
39
209
237
. 30265
292
320
690
722
. 31754
786
818
556
524
a 1492
460
429
328
319
310
301
293
25
24
23
22
21
824
816
807
40
680
708
. 28736
764
792
938
. 29970
.30001
033
065
402
367
3.3332
297
261
799
791
. 95782
20
40
348
376
403
431
459
850
882
914
946
. 31978
397
366
334
303
3. 1271
. 95284
275
260
257
248
20
41
42
43
19
18
17
16
41
42
43
44
19
44
774
766
O^f
18
17
16
45
46
47
820
847
875
903
931
097
128
160
192
224
226
191
156
122
087
757
749
740
732
724
15
14
13
12
11
45
46
47
48
49
. 30486
514
542
570
597
. 32010
042
074
106
139
240
209
178
146
115
240
231
222
213
204
15
14
13
12
11
48
49
50
959
. 28987
.29015
042
070
'255
. 30287
319
351
382
052
3. 3017
3. 2983
948
914
715
. 95707
698
690
10
9
50
625
653
680
. 30708
736
171
203
235
. 32267
299
084
053
3. 1022
3. 0991
9'61
. 95195
186
177
168
159
10
51
52
53
54
681
8
7
6
51
52
53
54
9
8
7
6
55
56
57
58
59
60
098
126
154
182
209
. 29237
414
446
478
509
541
. 30573
879
845
811
777
743
3. 2709
673
664
656
647
639
. 95630
5
4
3
2
1
0
55
56
57
58
59
60
7.63
791
819
846
874
.30902
331
363
396
428
460
. 32492
930
899
868
838
807
3. 0777
150
142
133
124
115
. 95106
5
4
3
2
1
0
cos
cot
tan
sin
1
cos
cot
tan
sin
/
73
72
10
Gen
erat
ed o
n 20
13-1
0-18
05:
34 G
MT
/ h
ttp:
//hdl
.han
dle.
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2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
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tized
/ h
ttp:
//ww
w.h
athi
trus
t.or
g/ac
cess
_use
#pd
-goo
gle
-
AIR NAVIGATION TABLES
Table I. Natural Trigonometric Functions Continued
18 19
'
sin
tan
cot
cos
'
sin
tan
cot
cos
0
.30902
929
957
. 30985
.31012
. 32492
524
556
3. 0777
746
716
686
655
. 95106
097
OSS
079
070
60
59
58
57
56
0
. 32557
584
612
639
667
.34433
465
498
530
563
2.9042
2.9015
2. 8987
960
933
. 94552
542
533
523
514
60
i
1
2
3
59
58
57
56
2
3
588
621
4
4
5
6
7
8
9
040
068
095
123
151
653
685
717
. 32749
782
625
595
565
535
a 0505
061
. 95052
043
033
55
54
53
52
5
6
7
8
9
694
722
749
. 32777
596
628
661
693
. 34726
905
878
851
824
797
.504
495
485
476
466
55
54
53
52
51
024
51
804
10
11
12
13
14
178
206
233
261
. 31289
814
846
878
911
943
475
445
415
385
356
015
.95006
. 94997
988
979
50
10
832
859
887
914
942
758
791
824
856
770
2.8743
716
689
662
. 94457
447
438
428
418
50
49
48
47
46
11
12
13
14
889
49
48
47
46
15
16
17
18
19
316
344
372
399
. 32975
.33007
040
072
326
970
961
952
943
933
45
44
43
42
41
15
16
17
18
19
969
. 32997
. 33024
051
079
922
954
. 34987
.35020
052
636
609
582
556
529
409
399
390
380
370
45
44
43
42
41
427
104
296
a 0267
237
208
20
454
482
. 31510
537
565
136
169
201
233
. 33266
178
149
120
090
061
. 94924
915
906
897
888
40
39
38
37
36
20
21
22
23
106
134
161
189
. 33216
085
118
150
183
216
2.8502
476
449
423
397
. 94361
351
342
332
322
40
21
22
23
24
24
39
38
37
36
25
26
27
28
29
593
620
648
675
703
298
330
363
395
032
3.0003
2. 9974
945
916
878
869
860
. 94851
842
35
34
33
32
31
25
244
271
298
326
353
.35248
281
314
346
379
370
344
318
291
2.8265
313
303
293
284
274
35
34
33
32
31
427
26
27
28
29
30
31
32
33
34
730
. 31758
786
813
460
. 33492
524
557
887
858
829
800
772
832
823
814
805
795
30
29
28
27
30
381
. 33408
436
463
490
412
. 35445
477
510
543
239
213
187
161
135
.94264
254
245
235
225
30
841
589
26
31
32
33
34
29
28
27
26
35
36
37
38
39
868
896
923
951
. 31979
621
654
686
. 33718
751
2.9743
714
686
657
629
786
.94777
768
758
749
25
24
23
22
21
35
36
37
38
39
518
545
573
.33600
627
576
608
641
674
. 35707
109
083
057
032
2. 8006
215
206
196
186
25
24
23
22
21
176
40
.32000
034
061
089
116
783
816
848
881
913
600
572
544
515
740
730
721
712
. 94702
20
19
18
17
16
40
41
655
682
710
737
764
740
772
805
838
871
2.7980
955
929
903
. 94167
157
147
137
127
20
41
42
43
44
42
43
19
18
17
16
2.9487
44
878
45
46
47
48
49
144
171
199
227
254
945
. 33978
.34010
043
075
459
431
403
375
347
693
684
674
665
656
15
14
13
12
11
45
46
47
48
49
. 33792
819
846
904
937
.35969
.36002
035
852
2. 7827
801
776
751
118
108
098,
.94088
078
15
14
13
12
11
874
901
50
. 32282
309
337
364
392
108
140
173
205
. 34238
319
2. 9291
263
235
208
646
637
. 94627
618
609
10
50
51
52
53
54
929
956
. 33983
.34011
038
068
101
134
167
. 36199
725
700
675
2.7650
625
068
058
049
039
10
51
52
53
54
9
8
7
9
8
7
6
6
029
55
56
57
58
59
60
419
447
474
502
529
. 32557
270
303
335
368
400
.34433
180
152
125
097
070
2.9042
599
590
580
571
561
. 94552
5
4
3
2
1
0
t>5
56
57
58
59
60
065
093
120
147
175
.34202
232
600
575
550
525
500
2. 7475
019
. 94009
. 93999
989
979
. 93969
5
4
3
2
1
0
265
298
331
364
. 36397
cos
cot
tan
sin
cos
cot
tan
sin
/
71 70
11
Gen
erat
ed o
n 20
13-1
0-18
05:
34 G
MT
/ h
ttp:
//hdl
.han
dle.
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2027
/uc1
.b32
4160
5Pu
blic
Dom
ain,
Goo
gle-
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tized
/ h
ttp:
//ww
