Table of Cos(θ)
Degree 0¯ 6¯ 12¯ 18¯ 24¯ 30¯ 36¯ 42¯ 48¯ 54¯ Different of minutes
0 0.1° 0.2° 0.3° 0.4° 0.5° 0.6° 0.7° 0.8° 0.9° 1¯ 2¯ 3¯ 4¯ 5¯
0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0 0 0 0 0
1 0.9998 0.9998 0.9998 0.9997 0.9997 0.9997 0.9996 0.9996 0.9995 0.9995 0 0 0 0 0
2 0.9994 0.9993 0.9993 0.9992 0.9991 0.9990 0.9990 0.9989 0.9988 0.9987 0 0 0 1 1
3 0.9986 0.9985 0.9984 0.9983 0.9982 0.9981 0.9980 0.9979 0.9978 0.9977 0 0 1 1 1
4 0.9975 0.9974 0.9973 0.9972 0.9971 0.9969 0.9968 0.9966 0.9965 0.9963 0 0 1 1 1
5 0.9962 0.9960 0.9959 0.9957 0.9956 0.9954 0.9952 0.9951 0.9949 0.9947 0 1 1 1 2
6 0.9945 0.9943 0.9942 0.9940 0.9938 0.9936 0.9934 0.9932 0.9930 0.9928 0 1 1 1 2
7 0.9925 0.9923 0.9921 0.9919 0.9917 0.9914 0.9912 0.9910 0.9907 0.9905 0 1 1 2 2
8 0.9902 0.9900 0.9898 0.9895 0.9893 0.9890 0.9888 0.9885 0.9882 0.9880 0 1 1 2 2
9 0.9876 0.9874 0.9871 0.9869 0.9866 0.9863 0.9860 0.9857 0.9854 0.9851 0 1 1 2 2
10 0.9848 0.9845 0.9842 0.9839 0.9836 0.9833 0.9829 0.9826 0.9823 0.9820 1 1 2 2 3
11 0.9816 0.9813 0.9810 0.9806 0.9803 0.9799 0.9796 0.9792 0.9789 0.9785 1 1 2 2 3
12 0.9781 0.9778 0.9774 0.9770 0.9767 0.9763 0.9759 0.9755 0.9751 0.9748 1 1 2 3 3
13 0.9743 0.9740 0.9736 0.9732 0.9728 0.9724 0.9720 0.9715 0.9711 0.9707 1 1 2 3 3
14 0.9702 0.9699 0.9694 0.9690 0.9686 0.9681 0.9677 0.9673 0.9668 0.9664 1 1 2 3 4
15 0.9659 0.9655 0.9650 0.9646 0.9641 0.9636 0.9632 0.9627 0.9622 0.9617 1 2 2 3 4
16 0.9612 0.9608 0.9603 0.9598 0.9593 0.9588 0.9583 0.9578 0.9573 0.9568 1 2 2 3 4
17 0.9562 0.9558 0.9553 0.9548 0.9542 0.9537 0.9532 0.9527 0.9521 0.9516 1 2 3 3 4
18 0.9510 0.9505 0.9500 0.9494 0.9489 0.9483 0.9478 0.9472 0.9466 0.9461 1 2 3 4 5
19 0.9454 0.9449 0.9444 0.9438 0.9432 0.9426 0.9421 0.9415 0.9409 0.9403 1 2 3 4 5
20 0.9396 0.9391 0.9385 0.9379 0.9373 0.9367 0.9361 0.9354 0.9348 0.9342 1 2 3 4 5
21 0.9335 0.9330 0.9323 0.9317 0.9311 0.9304 0.9298 0.9291 0.9285 0.9278 1 2 3 4 5
22 0.9271 0.9265 0.9259 0.9252 0.9245 0.9239 0.9232 0.9225 0.9219 0.9212 1 2 3 4 6
23 0.9204 0.9198 0.9191 0.9184 0.9178 0.9171 0.9164 0.9157 0.9150 0.9143 1 2 3 5 6
24 0.9134 0.9128 0.9121 0.9114 0.9107 0.9100 0.9092 0.9085 0.9078 0.9070 1 3 4 5 6
25 0.9062 0.9056 0.9048 0.9041 0.9033 0.9026 0.9018 0.9011 0.9003 0.8996 1 3 4 5 6
26 0.8987 0.8980 0.8973 0.8965 0.8957 0.8949 0.8942 0.8934 0.8926 0.8918 1 3 4 5 6
27 0.8909 0.8902 0.8894 0.8886 0.8878 0.8870 0.8862 0.8854 0.8846 0.8838 1 3 4 5 7
28 0.8828 0.8821 0.8813 0.8805 0.8796 0.8788 0.8780 0.8771 0.8763 0.8755 1 3 4 6 7
29 0.8745 0.8738 0.8729 0.8721 0.8712 0.8704 0.8695 0.8686 0.8678 0.8669 1 3 4 6 7
30 0.8659 0.8652 0.8643 0.8634 0.8625 0.8616 0.8607 0.8599 0.8590 0.8581 1 3 4 6 7
31 0.8570 0.8563 0.8554 0.8545 0.8536 0.8526 0.8517 0.8508 0.8499 0.8490 1 3 5 6 8
32 0.8479 0.8471 0.8462 0.8453 0.8443 0.8434 0.8425 0.8415 0.8406 0.8396 2 3 5 6 8
33 0.8385 0.8377 0.8368 0.8358 0.8348 0.8339 0.8329 0.8320 0.8310 0.8300 2 3 5 6 8
34 0.8289 0.8281 0.8271 0.8261 0.8251 0.8241 0.8231 0.8221 0.8211 0.8202 2 3 5 7 8
35 0.8190 0.8181 0.8171 0.8161 0.8151 0.8141 0.8131 0.8121 0.8111 0.8100 2 3 5 7 8
36 0.8089 0.8080 0.8070 0.8059 0.8049 0.8039 0.8028 0.8018 0.8007 0.7997 2 3 5 7 9
37 0.7985 0.7976 0.7965 0.7955 0.7944 0.7934 0.7923 0.7912 0.7902 0.7891 2 4 5 7 9
38 0.7879 0.7869 0.7859 0.7848 0.7837 0.7826 0.7815 0.7804 0.7793 0.7782 2 4 5 7 9
39 0.7770 0.7760 0.7749 0.7738 0.7727 0.7716 0.7705 0.7694 0.7683 0.7672 2 4 6 7 9
40 0.7659 0.7649 0.7638 0.7627 0.7615 0.7604 0.7593 0.7581 0.7570 0.7559 2 4 6 8 9
41 0.7546 0.7536 0.7524 0.7513 0.7501 0.7490 0.7478 0.7466 0.7455 0.7443 2 4 6 8 10
42 0.7430 0.7420 0.7408 0.7396 0.7385 0.7373 0.7361 0.7349 0.7337 0.7325 2 4 6 8 10
43 0.7312 0.7302 0.7290 0.7278 0.7266 0.7254 0.7242 0.7230 0.7218 0.7206 2 4 6 8 10
44 0.7192 0.7181 0.7169 0.7157 0.7145 0.7133 0.7120 0.7108 0.7096 0.7083 2 4 6 8 10
45 0.7070 0.7059 0.7046 0.7034 0.7022 0.7009 0.6997 0.6984 0.6972 0.6959 2 4 6 8 10
46 0.6945 0.6934 0.6921 0.6909 0.6896 0.6884 0.6871 0.6858 0.6845 0.6833 2 4 6 8 11
47 0.6819 0.6807 0.6794 0.6782 0.6769 0.6756 0.6743 0.6730 0.6717 0.6704 2 4 6 9 11
48 0.6690 0.6678 0.6665 0.6652 0.6639 0.6626 0.6613 0.6600 0.6587 0.6574 2 4 7 9 11
49 0.6559 0.6547 0.6534 0.6521 0.6508 0.6494 0.6481 0.6468 0.6455 0.6441 2 4 7 9 11
50 0.6426 0.6414 0.6401 0.6388 0.6374 0.6361 0.6347 0.6334 0.6320 0.6307 2 4 7 9 11
51 0.6292 0.6280 0.6266 0.6252 0.6239 0.6225 0.6211 0.6198 0.6184 0.6170 2 5 7 9 11
52 0.6155 0.6143 0.6129 0.6115 0.6101 0.6088 0.6074 0.6060 0.6046 0.6032 2 5 7 9 12
53 0.6017 0.6004 0.5990 0.5976 0.5962 0.5948 0.5934 0.5920 0.5906 0.5892 2 5 7 9 12
54 0.5876 0.5864 0.5850 0.5835 0.5821 0.5807 0.5793 0.5779 0.5764 0.5750 2 5 7 9 12
55 0.5734 0.5721 0.5707 0.5693 0.5678 0.5664 0.5650 0.5635 0.5621 0.5606 2 5 7 10 12
56 0.5591 0.5577 0.5563 0.5548 0.5534 0.5519 0.5505 0.5490 0.5476 0.5461 2 5 7 10 12
57 0.5445 0.5432 0.5417 0.5402 0.5388 0.5373 0.5358 0.5344 0.5329 0.5314 2 5 7 10 12
58 0.5298 0.5284 0.5270 0.5255 0.5240 0.5225 0.5210 0.5195 0.5180 0.5165 2 5 7 10 12
59 0.5149 0.5135 0.5120 0.5105 0.5090 0.5075 0.5060 0.5045 0.5030 0.5015 3 5 8 10 13
60 0.4999 0.4985 0.4970 0.4955 0.4939 0.4924 0.4909 0.4894 0.4879 0.4863 3 5 8 10 13
61 0.4847 0.4833 0.4818 0.4802 0.4787 0.4772 0.4756 0.4741 0.4726 0.4710 3 5 8 10 13
62 0.4693 0.4679 0.4664 0.4648 0.4633 0.4617 0.4602 0.4586 0.4571 0.4555 3 5 8 10 13
63 0.4539 0.4524 0.4509 0.4493 0.4478 0.4462 0.4446 0.4431 0.4415 0.4399 3 5 8 10 13
64 0.4383 0.4368 0.4352 0.4337 0.4321 0.4305 0.4289 0.4274 0.4258 0.4242 3 5 8 11 13
65 0.4225 0.4210 0.4195 0.4179 0.4163 0.4147 0.4131 0.4115 0.4099 0.4083 3 5 8 11 13
66 0.4066 0.4051 0.4035 0.4019 0.4003 0.3987 0.3971 0.3955 0.3939 0.3923 3 5 8 11 14
67 0.3906 0.3891 0.3875 0.3859 0.3843 0.3827 0.3811 0.3795 0.3778 0.3762 3 5 8 11 14
68 0.3745 0.3730 0.3714 0.3697 0.3681 0.3665 0.3649 0.3633 0.3616 0.3600 3 5 8 11 14
69 0.3583 0.3567 0.3551 0.3535 0.3518 0.3502 0.3486 0.3469 0.3453 0.3437 3 5 8 11 14
70 0.3419 0.3404 0.3387 0.3371 0.3355 0.3338 0.3322 0.3305 0.3289 0.3272 3 5 8 11 14
71 0.3255 0.3239 0.3223 0.3206 0.3190 0.3173 0.3156 0.3140 0.3123 0.3107 3 6 8 11 14
72 0.3089 0.3074 0.3057 0.3040 0.3024 0.3007 0.2990 0.2974 0.2957 0.2940 3 6 8 11 14
73 0.2923 0.2907 0.2890 0.2874 0.2857 0.2840 0.2823 0.2807 0.2790 0.2773 3 6 8 11 14
74 0.2756 0.2740 0.2723 0.2706 0.2689 0.2672 0.2656 0.2639 0.2622 0.2605 3 6 8 11 14
75 0.2587 0.2571 0.2554 0.2538 0.2521 0.2504 0.2487 0.2470 0.2453 0.2436 3 6 8 11 14
76 0.2418 0.2402 0.2385 0.2368 0.2351 0.2334 0.2317 0.2300 0.2284 0.2267 3 6 8 11 14
77 0.2249 0.2233 0.2215 0.2198 0.2181 0.2164 0.2147 0.2130 0.2113 0.2096 3 6 9 11 14
78 0.2078 0.2062 0.2045 0.2028 0.2011 0.1994 0.1977 0.1959 0.1942 0.1925 3 6 9 11 14
79 0.1907 0.1891 0.1874 0.1857 0.1840 0.1822 0.1805 0.1788 0.1771 0.1754 3 6 9 11 14
80 0.1736 0.1719 0.1702 0.1685 0.1668 0.1650 0.1633 0.1616 0.1599 0.1582 3 6 9 12 14
81 0.1564 0.1547 0.1530 0.1513 0.1495 0.1478 0.1461 0.1444 0.1426 0.1409 3 6 9 12 14
82 0.1391 0.1374 0.1357 0.1340 0.1323 0.1305 0.1288 0.1271 0.1253 0.1236 3 6 9 12 14
83 0.1218 0.1201 0.1184 0.1167 0.1149 0.1132 0.1115 0.1097 0.1080 0.1063 3 6 9 12 14
84 0.1045 0.1028 0.1011 0.0993 0.0976 0.0958 0.0941 0.0924 0.0906 0.0889 3 6 9 12 14
85 0.0871 0.0854 0.0837 0.0819 0.0802 0.0785 0.0767 0.0750 0.0732 0.0715 3 6 9 12 14
86 0.0697 0.0680 0.0663 0.0645 0.0628 0.0610 0.0593 0.0576 0.0558 0.0541 3 6 9 12 15
87 0.0523 0.0506 0.0488 0.0471 0.0454 0.0436 0.0419 0.0401 0.0384 0.0366 3 6 9 12 15
88 0.0349 0.0332 0.0314 0.0297 0.0279 0.0262 0.0244 0.0227 0.0209 0.0192 3 6 9 12 15
89 0.0174 0.0157 0.0140 0.0122 0.0105 0.0087 0.0070 0.0052 0.0035 0.0017 3 6 9 12 15