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Bradis Table: Sines, Cosines, Tangents, Cotangents

The Bradis table is a reference resource containing values of sines, cosines, tangents and cotangents for angles from 0° to 90° with a step of 1 minute. The table is essential for solving problems in trigonometry, geometry and physics, as well as for preparing for the EGE and OGE exams. Please note that the tables presented here are enhanced versions with values based on modern (more accurate) calculation algorithms.

About this reference

  • The values are calculated using standard trigonometric formulas and correspond to the classic four-digit tables by V. M. Bradis.
  • Modern mathematical libraries were used to verify accuracy (precision up to 4 decimal places).
  • This material was prepared by a mathematics teacher and is intended for schoolchildren, university students, and anyone preparing for exams.

On this page:

Bradis table online: trigonometric calculator

Enter an angle in degrees to get the values of sin, cos, tan and cot. The calculator works online in real time and provides values accurate to 6 decimal places. If the angle you need is not in the Bradis table, use this calculator.

For example: 30, 45, 32.5, 15.25

Key values of trigonometric functions

These values should be memorized — they frequently appear on exams.

Angle sin cos tg ctg
0°010∞
30°0.50000.86600.57741.7321
45°0.70710.707111
60°0.86600.50001.73210.5774
90°10∞0

History of the Bradis tables

The Bradis tables were created by the outstanding Soviet mathematician and educator Vladimir Modestovich Bradis (1890–1975). The first edition of these tables was published in 1921.

Vladimir Modestovich Bradis was born in Pskov and received his education at St. Petersburg University. He devoted most of his scientific career to developing methods for simplifying mathematical calculations and to teaching mathematics.

The four-digit Bradis mathematical tables quickly became a standard tool for engineering and scientific calculations in the USSR, and later in many other countries. Their popularity was due to the optimal balance between accuracy (four significant digits) and ease of use.

For decades, they were indispensable assistants for engineers, physicists, astronomers and students, until they were superseded by electronic calculators.

Examples of using the Bradis table

Example 1. Find sin 30°

In the sine table, find the row for 30° and the intersection with the column 0′ — we get 0.5000.

Answer: sin 30° = 0.5000.

Example 2. Find sin 32°27′

In the table, we find the nearest values:

  • sin 32°24′ = 0.5358
  • sin 32°30′ = 0.5373

The difference between the values: 0.5373 − 0.5358 = 0.0015.

For 27′ from 24′, the difference is 3 minutes. Correction: 0.0015 × (3/6) = 0.00075.

Total: 0.5358 + 0.00075 = 0.5366.

Answer: sin 32°27′ ≈ 0.5366.

Example 3. Find tg 45°

In the tangent table, find the row for 45° and the intersection with the column 0′ — we get 1.0000.

Answer: tan 45° = 1.0000.

Complete Bradis table for sines and cosines

Note that the values of sines and cosines of angles cannot be greater than 1.

How to read the table: the row represents degrees, the column represents minutes (0′, 6′, 12′ … 60′). The last three columns (1′, 2′, 3′) are corrections: they are added to the sine value and subtracted from the cosine value if the angle is not a multiple of 6 minutes.

sin 0′ 6′ 12′ 18′ 24′ 30′ 36′ 42′ 48′ 54′ 60′   1′ 2′ 3′
  0.0000 90°  
0° 0.0000 0.0017 0.0035 0.0052 0.0070 0.0087 0.0105 0.0122 0.0140 0.0157 0.0175 89° 3 6 9
1° 0.0175 0.0192 0.0209 0.0227 0.0244 0.0262 0.0279 0.0297 0.0314 0.0332 0.0349 88° 3 6 9
2° 0.0349 0.0366 0.0384 0.0401 0.0419 0.0436 0.0454 0.0471 0.0488 0.0506 0.0523 87° 3 6 9
3° 0.0523 0.0541 0.0558 0.0576 0.0593 0.0610 0.0628 0.0645 0.0663 0.0680 0.0698 86° 3 6 9
4° 0.0698 0.0715 0.0732 0.0750 0.0767 0.0785 0.0802 0.0819 0.0837 0.0854 0.0872 85° 3 6 9
5° 0.0872 0.0889 0.0906 0.0924 0.0941 0.0958 0.0976 0.0993 0.1011 0.1028 0.1045 84° 3 6 9
6° 0.1045 0.1063 0.1080 0.1097 0.1115 0.1132 0.1149 0.1167 0.1184 0.1201 0.1219 83° 3 6 9
7° 0.1219 0.1236 0.1253 0.1271 0.1288 0.1305 0.1323 0.1340 0.1357 0.1374 0.1392 82° 3 6 9
8° 0.1392 0.1409 0.1426 0.1444 0.1461 0.1478 0.1495 0.1513 0.1530 0.1547 0.1564 81° 3 6 9
9° 0.1564 0.1582 0.1599 0.1616 0.1633 0.1650 0.1668 0.1685 0.1702 0.1719 0.1736 80° 3 6 9
10° 0.1736 0.1754 0.1771 0.1788 0.1805 0.1822 0.1840 0.1857 0.1874 0.1891 0.1908 79° 3 6 9
11° 0.1908 0.1925 0.1942 0.1959 0.1977 0.1994 0.2011 0.2028 0.2045 0.2062 0.2079 78° 3 6 9
12° 0.2079 0.2096 0.2113 0.2130 0.2147 0.2164 0.2181 0.2198 0.2215 0.2233 0.2250 77° 3 6 9
13° 0.2250 0.2267 0.2284 0.2300 0.2317 0.2334 0.2351 0.2368 0.2385 0.2402 0.2419 76° 3 6 9
14° 0.2419 0.2436 0.2453 0.2470 0.2487 0.2504 0.2521 0.2538 0.2554 0.2571 0.2588 75° 3 6 8
15° 0.2588 0.2605 0.2622 0.2639 0.2656 0.2672 0.2689 0.2706 0.2723 0.2740 0.2756 74° 3 6 8
16° 0.2756 0.2773 0.2790 0.2807 0.2823 0.2840 0.2857 0.2874 0.2890 0.2907 0.2924 73° 3 6 8
17° 0.2924 0.2940 0.2957 0.2974 0.2990 0.3007 0.3024 0.3040 0.3057 0.3074 0.3090 72° 3 6 8
18° 0.3090 0.3107 0.3123 0.3140 0.3156 0.3173 0.3190 0.3206 0.3223 0.3239 0.3256 71° 3 6 8
19° 0.3256 0.3272 0.3289 0.3305 0.3322 0.3338 0.3355 0.3371 0.3387 0.3404 0.3420 70° 3 6 8
20° 0.3420 0.3437 0.3453 0.3469 0.3486 0.3502 0.3518 0.3535 0.3551 0.3567 0.3584 69° 3 5 8
21° 0.3584 0.3600 0.3616 0.3633 0.3649 0.3665 0.3681 0.3697 0.3714 0.3730 0.3746 68° 3 5 8
22° 0.3746 0.3762 0.3778 0.3795 0.3811 0.3827 0.3843 0.3859 0.3875 0.3891 0.3907 67° 3 5 8
23° 0.3907 0.3923 0.3939 0.3955 0.3971 0.3987 0.4003 0.4019 0.4035 0.4051 0.4067 66° 3 5 8
24° 0.4067 0.4083 0.4099 0.4115 0.4131 0.4147 0.4163 0.4179 0.4195 0.4210 0.4226 65° 3 5 8
25° 0.4226 0.4242 0.4258 0.4274 0.4289 0.4305 0.4321 0.4337 0.4352 0.4368 0.4384 64° 3 5 8
26° 0.4384 0.4399 0.4415 0.4431 0.4446 0.4462 0.4478 0.4493 0.4509 0.4524 0.4540 63° 3 5 8
27° 0.4540 0.4555 0.4571 0.4586 0.4602 0.4617 0.4633 0.4648 0.4664 0.4679 0.4695 62° 3 5 8
28° 0.4695 0.4710 0.4726 0.4741 0.4756 0.4772 0.4787 0.4802 0.4818 0.4833 0.4848 61° 3 5 8
29° 0.4848 0.4863 0.4879 0.4894 0.4909 0.4924 0.4939 0.4955 0.4970 0.4985 0.5000 60° 3 5 8
30° 0.5000 0.5015 0.5030 0.5045 0.5060 0.5075 0.5090 0.5105 0.5120 0.5135 0.5150 59° 3 5 8
31° 0.5150 0.5165 0.5180 0.5195 0.5210 0.5225 0.5240 0.5255 0.5270 0.5284 0.5299 58° 2 5 7
32° 0.5299 0.5314 0.5329 0.5344 0.5358 0.5373 0.5388 0.5402 0.5417 0.5432 0.5446 57° 2 5 7
33° 0.5446 0.5461 0.5476 0.5490 0.5505 0.5519 0.5534 0.5548 0.5563 0.5577 0.5592 56° 2 5 7
34° 0.5592 0.5606 0.5621 0.5635 0.5650 0.5664 0.5678 0.5693 0.5707 0.5721 0.5736 55° 2 5 7
35° 0.5736 0.5750 0.5764 0.5779 0.5793 0.5807 0.5821 0.5835 0.5850 0.5864 0.5878 54° 2 5 7
36° 0.5878 0.5892 0.5906 0.5920 0.5934 0.5948 0.5962 0.5976 0.5990 0.6004 0.6018 53° 2 5 7
37° 0.6018 0.6032 0.6046 0.6060 0.6074 0.6088 0.6101 0.6115 0.6129 0.6143 0.6157 52° 2 5 7
38° 0.6157 0.6170 0.6184 0.6198 0.6211 0.6225 0.6239 0.6252 0.6266 0.6280 0.6293 51° 2 5 7
39° 0.6293 0.6307 0.6320 0.6334 0.6347 0.6361 0.6374 0.6388 0.6401 0.6414 0.6428 50° 2 5 7
40° 0.6428 0.6441 0.6455 0.6468 0.6481 0.6494 0.6508 0.6521 0.6534 0.6547 0.6561 49° 2 4 7
41° 0.6561 0.6574 0.6587 0.6600 0.6613 0.6626 0.6639 0.6652 0.6665 0.6678 0.6691 48° 2 4 7
42° 0.6691 0.6704 0.6717 0.6730 0.6743 0.6756 0.6769 0.6782 0.6794 0.6807 0.6820 47° 2 4 6
43° 0.6820 0.6833 0.6845 0.6858 0.6871 0.6884 0.6896 0.6909 0.6921 0.6934 0.6947 46° 2 4 6
44° 0.6947 0.6959 0.6972 0.6984 0.6997 0.7009 0.7022 0.7034 0.7046 0.7059 0.7071 45° 2 4 6
45° 0.7071 0.7083 0.7096 0.7108 0.7120 0.7133 0.7145 0.7157 0.7169 0.7181 0.7193 44° 2 4 6
46° 0.7193 0.7206 0.7218 0.7230 0.7242 0.7254 0.7266 0.7278 0.7290 0.7302 0.7314 43° 2 4 6
47° 0.7314 0.7325 0.7337 0.7349 0.7361 0.7373 0.7385 0.7396 0.7408 0.7420 0.7431 42° 2 4 6
48° 0.7431 0.7443 0.7455 0.7466 0.7478 0.7490 0.7501 0.7513 0.7524 0.7536 0.7547 41° 2 4 6
49° 0.7547 0.7559 0.7570 0.7581 0.7593 0.7604 0.7615 0.7627 0.7638 0.7649 0.7660 40° 2 4 6
50° 0.7660 0.7672 0.7683 0.7694 0.7705 0.7716 0.7727 0.7738 0.7749 0.7760 0.7771 39° 2 4 6
51° 0.7771 0.7782 0.7793 0.7804 0.7815 0.7826 0.7837 0.7848 0.7859 0.7869 0.7880 38° 2 4 5
52° 0.7880 0.7891 0.7902 0.7912 0.7923 0.7934 0.7944 0.7955 0.7965 0.7976 0.7986 37° 2 4 5
53° 0.7986 0.7997 0.8007 0.8018 0.8028 0.8039 0.8049 0.8059 0.8070 0.8080 0.8090 36° 2 3 5
54° 0.8090 0.8100 0.8111 0.8121 0.8131 0.8141 0.8151 0.8161 0.8171 0.8181 0.8192 35° 2 3 5
55° 0.8192 0.8202 0.8211 0.8221 0.8231 0.8241 0.8251 0.8261 0.8271 0.8281 0.8290 34° 2 3 5
56° 0.8290 0.8300 0.8310 0.8320 0.8329 0.8339 0.8348 0.8358 0.8368 0.8377 0.8387 33° 2 3 5
57° 0.8387 0.8396 0.8406 0.8415 0.8425 0.8434 0.8443 0.8453 0.8462 0.8471 0.8480 32° 2 3 5
58° 0.8480 0.8490 0.8499 0.8508 0.8517 0.8526 0.8536 0.8545 0.8554 0.8563 0.8572 31° 2 3 5
59° 0.8572 0.8581 0.8590 0.8599 0.8607 0.8616 0.8625 0.8634 0.8643 0.8652 0.8660 30° 1 3 4
60° 0.8660 0.8669 0.8678 0.8686 0.8695 0.8704 0.8712 0.8721 0.8729 0.8738 0.8746 29° 1 3 4
61° 0.8746 0.8755 0.8763 0.8771 0.8780 0.8788 0.8796 0.8805 0.8813 0.8821 0.8829 28° 1 3 4
62° 0.8829 0.8838 0.8846 0.8854 0.8862 0.8870 0.8878 0.8886 0.8894 0.8902 0.8910 27° 1 3 4
63° 0.8910 0.8918 0.8926 0.8934 0.8942 0.8949 0.8957 0.8965 0.8973 0.8980 0.8988 26° 1 3 4
64° 0.8988 0.8996 0.9003 0.9011 0.9018 0.9026 0.9033 0.9041 0.9048 0.9056 0.9063 25° 1 3 4
65° 0.9063 0.9070 0.9078 0.9085 0.9092 0.9100 0.9107 0.9114 0.9121 0.9128 0.9135 24° 1 2 4
66° 0.9135 0.9143 0.9150 0.9157 0.9164 0.9171 0.9178 0.9184 0.9191 0.9198 0.9205 23° 1 2 4
67° 0.9205 0.9212 0.9219 0.9225 0.9232 0.9239 0.9245 0.9252 0.9259 0.9265 0.9272 22° 1 2 3
68° 0.9272 0.9278 0.9285 0.9291 0.9298 0.9304 0.9311 0.9317 0.9323 0.9330 0.9336 21° 1 2 3
69° 0.9336 0.9342 0.9348 0.9354 0.9361 0.9367 0.9373 0.9379 0.9385 0.9391 0.9397 20° 1 2 3
70° 0.9397 0.9403 0.9409 0.9415 0.9421 0.9426 0.9432 0.9438 0.9444 0.9449 0.9455 19° 1 2 3
71° 0.9455 0.9461 0.9466 0.9472 0.9478 0.9483 0.9489 0.9494 0.9500 0.9505 0.9511 18° 1 2 3
72° 0.9511 0.9516 0.9521 0.9527 0.9532 0.9537 0.9542 0.9548 0.9553 0.9558 0.9563 17° 1 2 3
73° 0.9563 0.9568 0.9573 0.9578 0.9583 0.9588 0.9593 0.9598 0.9603 0.9608 0.9613 16° 1 2 3
74° 0.9613 0.9617 0.9622 0.9627 0.9632 0.9636 0.9641 0.9646 0.9650 0.9655 0.9659 15° 1 2 2
75° 0.9659 0.9664 0.9668 0.9673 0.9677 0.9681 0.9686 0.9690 0.9694 0.9699 0.9703 14° 1 2 2
76° 0.9703 0.9707 0.9711 0.9715 0.9720 0.9724 0.9728 0.9732 0.9736 0.9740 0.9744 13° 1 1 2
77° 0.9744 0.9748 0.9751 0.9755 0.9759 0.9763 0.9767 0.9770 0.9774 0.9778 0.9781 12° 1 1 2
78° 0.9781 0.9785 0.9789 0.9792 0.9796 0.9799 0.9803 0.9806 0.9810 0.9813 0.9816 11° 1 1 2
79° 0.9816 0.9820 0.9823 0.9826 0.9829 0.9833 0.9836 0.9839 0.9842 0.9845 0.9848 10° 1 1 2
80° 0.9848 0.9851 0.9854 0.9857 0.9860 0.9863 0.9866 0.9869 0.9871 0.9874 0.9877 9° 1 1 2
81° 0.9877 0.9880 0.9882 0.9885 0.9888 0.9890 0.9893 0.9895 0.9898 0.9900 0.9903 8° 0 1 1
82° 0.9903 0.9905 0.9907 0.9910 0.9912 0.9914 0.9917 0.9919 0.9921 0.9923 0.9925 7° 0 1 1
83° 0.9925 0.9928 0.9930 0.9932 0.9934 0.9936 0.9938 0.9940 0.9942 0.9943 0.9945 6° 0 1 1
84° 0.9945 0.9947 0.9949 0.9951 0.9952 0.9954 0.9956 0.9957 0.9959 0.9960 0.9962 5° 0 1 1
85° 0.9962 0.9963 0.9965 0.9966 0.9968 0.9969 0.9971 0.9972 0.9973 0.9974 0.9976 4° 0 1 1
86° 0.9976 0.9977 0.9978 0.9979 0.9980 0.9981 0.9982 0.9983 0.9984 0.9985 0.9986 3° 0 0 1
87° 0.9986 0.9987 0.9988 0.9989 0.9990 0.9990 0.9991 0.9992 0.9993 0.9993 0.9994 2° 0 0 0
88° 0.9994 0.9995 0.9995 0.9996 0.9996 0.9997 0.9997 0.9997 0.9998 0.9998 0.9998 1° 0 0 0
89° 0.9998 0.9999 0.9999 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0° 0 0 0
90° 1.0000  
  60′ 54′ 48′ 42′ 36′ 30′ 24′ 18′ 12′ 6′ 0′ cos 1′ 2′ 3′


Complete Bradis table for tangents and cotangents

How to read the table: the row represents degrees, the column represents minutes. The corrections in the last three columns are added to the tangent value (and subtracted from the cotangent value) if the angle is not a multiple of 6 minutes.

tg 0′ 6′ 12′ 18′ 24′ 30′ 36′ 42′ 48′ 54′ 60′   1′ 2′ 3′
  0.0000 90°  
0° 0.0000 0.0017 0.0035 0.0052 0.0070 0.0087 0.0105 0.0122 0.0140 0.0157 0.0175 89° 3 6 9
1° 0.0175 0.0192 0.0209 0.0227 0.0244 0.0262 0.0279 0.0297 0.0314 0.0332 0.0349 88° 3 6 9
2° 0.0349 0.0367 0.0384 0.0402 0.0419 0.0437 0.0454 0.0472 0.0489 0.0507 0.0524 87° 3 6 9
3° 0.0524 0.0542 0.0559 0.0577 0.0594 0.0612 0.0629 0.0647 0.0664 0.0682 0.0699 86° 3 6 9
4° 0.0699 0.0717 0.0734 0.0752 0.0769 0.0787 0.0805 0.0822 0.0840 0.0857 0.0875 85° 3 6 9
5° 0.0875 0.0892 0.0910 0.0928 0.0945 0.0963 0.0981 0.0998 0.1016 0.1033 0.1051 84° 3 6 9
6° 0.1051 0.1069 0.1086 0.1104 0.1122 0.1139 0.1157 0.1175 0.1192 0.1210 0.1228 83° 3 6 9
7° 0.1228 0.1246 0.1263 0.1281 0.1299 0.1317 0.1334 0.1352 0.1370 0.1388 0.1405 82° 3 6 9
8° 0.1405 0.1423 0.1441 0.1459 0.1477 0.1495 0.1512 0.1530 0.1548 0.1566 0.1584 81° 3 6 9
9° 0.1584 0.1602 0.1620 0.1638 0.1655 0.1673 0.1691 0.1709 0.1727 0.1745 0.1763 80° 3 6 9
10° 0.1763 0.1781 0.1799 0.1817 0.1835 0.1853 0.1871 0.1890 0.1908 0.1926 0.1944 79° 3 6 9
11° 0.1944 0.1962 0.1980 0.1998 0.2016 0.2035 0.2053 0.2071 0.2089 0.2107 0.2126 78° 3 6 9
12° 0.2126 0.2144 0.2162 0.2180 0.2199 0.2217 0.2235 0.2254 0.2272 0.2290 0.2309 77° 3 6 9
13° 0.2309 0.2327 0.2345 0.2364 0.2382 0.2401 0.2419 0.2438 0.2456 0.2475 0.2493 76° 3 6 9
14° 0.2493 0.2512 0.2530 0.2549 0.2568 0.2586 0.2605 0.2623 0.2642 0.2661 0.2679 75° 3 6 9
15° 0.2679 0.2698 0.2717 0.2736 0.2754 0.2773 0.2792 0.2811 0.2830 0.2849 0.2867 74° 3 6 9
16° 0.2867 0.2886 0.2905 0.2924 0.2943 0.2962 0.2981 0.3000 0.3019 0.3038 0.3057 73° 3 6 9
17° 0.3057 0.3076 0.3096 0.3115 0.3134 0.3153 0.3172 0.3191 0.3211 0.3230 0.3249 72° 3 6 10
18° 0.3249 0.3269 0.3288 0.3307 0.3327 0.3346 0.3365 0.3385 0.3404 0.3424 0.3443 71° 3 6 10
19° 0.3443 0.3463 0.3482 0.3502 0.3522 0.3541 0.3561 0.3581 0.3600 0.3620 0.3640 70° 3 7 10
20° 0.3640 0.3659 0.3679 0.3699 0.3719 0.3739 0.3759 0.3779 0.3799 0.3819 0.3839 69° 3 7 10
21° 0.3839 0.3859 0.3879 0.3899 0.3919 0.3939 0.3959 0.3979 0.4000 0.4020 0.4040 68° 3 7 10
22° 0.4040 0.4061 0.4081 0.4101 0.4122 0.4142 0.4163 0.4183 0.4204 0.4224 0.4245 67° 3 7 10
23° 0.4245 0.4265 0.4286 0.4307 0.4327 0.4348 0.4369 0.4390 0.4411 0.4431 0.4452 66° 3 7 10
24° 0.4452 0.4473 0.4494 0.4515 0.4536 0.4557 0.4578 0.4599 0.4621 0.4642 0.4663 65° 3 7 10
25° 0.4663 0.4684 0.4706 0.4727 0.4748 0.4770 0.4791 0.4813 0.4834 0.4856 0.4877 64° 4 7 11
26° 0.4877 0.4899 0.4921 0.4942 0.4964 0.4986 0.5008 0.5029 0.5051 0.5073 0.5095 63° 4 7 11
27° 0.5095 0.5117 0.5139 0.5161 0.5184 0.5206 0.5228 0.5250 0.5272 0.5295 0.5317 62° 4 7 11
28° 0.5317 0.5340 0.5362 0.5384 0.5407 0.5430 0.5452 0.5475 0.5498 0.5520 0.5543 61° 4 7 11
29° 0.5543 0.5566 0.5589 0.5612 0.5635 0.5658 0.5681 0.5704 0.5727 0.5750 0.5774 60° 4 8 11
30° 0.5774 0.5797 0.5820 0.5844 0.5867 0.5890 0.5914 0.5938 0.5961 0.5985 0.6009 59° 4 8 12
31° 0.6009 0.6032 0.6056 0.6080 0.6104 0.6128 0.6152 0.6176 0.6200 0.6224 0.6249 58° 4 8 12
32° 0.6249 0.6273 0.6297 0.6322 0.6346 0.6371 0.6395 0.6420 0.6445 0.6469 0.6494 57° 4 8 12
33° 0.6494 0.6519 0.6544 0.6569 0.6594 0.6619 0.6644 0.6669 0.6694 0.6720 0.6745 56° 4 8 12
34° 0.6745 0.6771 0.6796 0.6822 0.6847 0.6873 0.6899 0.6924 0.6950 0.6976 0.7002 55° 4 8 13
35° 0.7002 0.7028 0.7054 0.7080 0.7107 0.7133 0.7159 0.7186 0.7212 0.7239 0.7265 54° 4 9 13
36° 0.7265 0.7292 0.7319 0.7346 0.7373 0.7400 0.7427 0.7454 0.7481 0.7508 0.7536 53° 4 9 13
37° 0.7536 0.7563 0.7590 0.7618 0.7646 0.7673 0.7701 0.7729 0.7757 0.7785 0.7813 52° 5 9 14
38° 0.7813 0.7841 0.7869 0.7898 0.7926 0.7954 0.7983 0.8012 0.8040 0.8069 0.8098 51° 5 9 14
39° 0.8098 0.8127 0.8156 0.8185 0.8214 0.8243 0.8273 0.8302 0.8332 0.8361 0.8391 50° 5 10 14
40° 0.8391 0.8421 0.8451 0.8481 0.8511 0.8541 0.8571 0.8601 0.8632 0.8662 0.8693 49° 5 10 15
41° 0.8693 0.8724 0.8754 0.8785 0.8816 0.8847 0.8878 0.8910 0.8941 0.8972 0.9004 48° 5 10 15
42° 0.9004 0.9036 0.9067 0.9099 0.9131 0.9163 0.9195 0.9228 0.9260 0.9293 0.9325 47° 5 11 16
43° 0.9325 0.9358 0.9391 0.9424 0.9457 0.9490 0.9523 0.9556 0.9590 0.9623 0.9657 46° 5 11 16
44° 0.9657 0.9691 0.9725 0.9759 0.9793 0.9827 0.9861 0.9896 0.9930 0.9965 1.0000 45° 6 11 17
45° 1.0000 1.0035 1.0070 1.0105 1.0141 1.0176 1.0212 1.0247 1.0283 1.0319 1.0355 44° 6 12 17
46° 1.0355 1.0392 1.0428 1.0464 1.0501 1.0538 1.0575 1.0612 1.0649 1.0686 1.0724 43° 6 12 18
47° 1.0724 1.0761 1.0799 1.0837 1.0875 1.0913 1.0951 1.0990 1.1028 1.1067 1.1106 42° 6 13 19
48° 1.1106 1.1145 1.1184 1.1224 1.1263 1.1303 1.1343 1.1383 1.1423 1.1463 1.1504 41° 6 13 20
49° 1.1504 1.1544 1.1585 1.1626 1.1667 1.1708 1.1750 1.1792 1.1833 1.1875 1.1918 40° 7 14 20
50° 1.1918 1.1960 1.2002 1.2045 1.2088 1.2131 1.2174 1.2218 1.2261 1.2305 1.2349 39° 7 14 21
51° 1.2349 1.2393 1.2437 1.2482 1.2527 1.2572 1.2617 1.2662 1.2708 1.2753 1.2799 38° 7 15 22
52° 1.2799 1.2846 1.2892 1.2938 1.2985 1.3032 1.3079 1.3127 1.3175 1.3222 1.3270 37° 8 15 23
53° 1.3270 1.3319 1.3367 1.3416 1.3465 1.3514 1.3564 1.3613 1.3663 1.3713 1.3764 36° 8 16 24
54° 1.3764 1.3814 1.3865 1.3916 1.3968 1.4019 1.4071 1.4124 1.4176 1.4229 1.4281 35° 8 17 25
55° 1.4281 1.4335 1.4388 1.4442 1.4496 1.4550 1.4605 1.4659 1.4715 1.4770 1.4826 34° 9 18 27
56° 1.4826 1.4882 1.4938 1.4994 1.5051 1.5108 1.5166 1.5224 1.5282 1.5340 1.5399 33° 9 19 28
57° 1.5399 1.5458 1.5517 1.5577 1.5637 1.5697 1.5757 1.5818 1.5880 1.5941 1.6003 32° 10 20 29
58° 1.6003 1.6066 1.6128 1.6191 1.6255 1.6319 1.6383 1.6447 1.6512 1.6577 1.6643 31° 10 21 31
59° 1.6643 1.6709 1.6775 1.6842 1.6909 1.6977 1.7045 1.7113 1.7182 1.7251 1.7321 30° 11 22 33
60° 1.7321 1.7391 1.7461 1.7532 1.7603 1.7675 1.7747 1.7820 1.7893 1.7966 1.8040 29° 12 23 35
61° 1.8040 1.8115 1.8190 1.8265 1.8341 1.8418 1.8495 1.8572 1.8650 1.8728 1.8807 28° 12 25 37
62° 1.8807 1.8887 1.8967 1.9047 1.9128 1.9210 1.9292 1.9375 1.9458 1.9542 1.9626 27° 13 26 40
63° 1.9626 1.9711 1.9797 1.9883 1.9970 2.0057 2.0145 2.0233 2.0323 2.0413 2.0503 26° 14 28 42
64° 2.0503 2.0594 2.0686 2.0778 2.0872 2.0965 2.1060 2.1155 2.1251 2.1348 2.1445 25° 15 30 45
65° 2.1445 2.1543 2.1642 2.1742 2.1842 2.1943 2.2045 2.2148 2.2251 2.2355 2.2460 24° 16 33 49
66° 2.2460 2.2566 2.2673 2.2781 2.2889 2.2998 2.3109 2.3220 2.3332 2.3445 2.3559 23° 18 35 53
67° 2.3559 2.3673 2.3789 2.3906 2.4023 2.4142 2.4262 2.4383 2.4504 2.4627 2.4751 22° 19 38 57
68° 2.4751 2.4876 2.5002 2.5129 2.5257 2.5386 2.5517 2.5649 2.5782 2.5916 2.6051 21° 21 42 62
69° 2.6051 2.6187 2.6325 2.6464 2.6605 2.6746 2.6889 2.7034 2.7179 2.7326 2.7475 20° 23 45 68
70° 2.7475 2.7625 2.7776 2.7929 2.8083 2.8239 2.8397 2.8556 2.8716 2.8878 2.9042 19° 25 50 75
71° 2.9042 2.9208 2.9375 2.9544 2.9714 2.9887 3.0061 3.0237 3.0415 3.0595 3.0777 18° 27 55 83
72° 3.0777 3.0961 3.1146 3.1334 3.1524 3.1716 3.1910 3.2106 3.2305 3.2506 3.2709 17° 30 61 92
73° 3.2709 3.2914 3.3122 3.3332 3.3544 3.3759 3.3977 3.4197 3.4420 3.4646 3.4874 16° 34 68 102
74° 3.4874 3.5105 3.5339 3.5576 3.5816 3.6059 3.6305 3.6554 3.6806 3.7062 3.7321 15° 38 77 115
75° 3.7321 3.7583 3.7848 3.8118 3.8391 3.8667 3.8947 3.9232 3.9520 3.9812 4.0108 14° 43 87 131
  60′ 54′ 48′ 42′ 36′ 30′ 24′ 18′ 12′ 6′ 0′ ctg 1′ 2′ 3′

How to use the Bradis table: step-by-step instructions

  1. Find the row with the required number of degrees.
  2. Find the column with the required number of minutes (0′, 6′, 12′ … 60′).
  3. At the intersection — the value of the function. If the angle is not a multiple of 6′, use the corrections from the last three columns.
  4. Remember: for sine and tangent, the correction is added; for cosine and cotangent, it is subtracted.

Detailed instructions with pictures: How to use the Bradis table.

Download and print the Bradis table

Save the table in a convenient format for offline use or print it out to use as a cheat sheet:

The file contains both tables (sines/cosines and tangents/cotangents) with corrections. Suitable for printing on A4 paper and using as a cheat sheet during an exam.

Bradis table in 9th grade

In the 9th grade, the Bradis table is used when studying trigonometry and solving geometry problems. Students work with sines, cosines, tangents and cotangents of angles from 0° to 90°, and also learn to apply reduction formulas for angles greater than 90°.

Most often, the Bradis table in the 9th grade is needed for:

  • solving right triangles (using known sides and angles);
  • finding the values of trigonometric functions when solving problems on similarity and area;
  • preparing for the OGE in mathematics — trigonometry problems appear in the geometry section.

If you need the Bradis table for printing — use the link in the "Download and print" section above.

Frequently asked questions about the Bradis table

What is the Bradis table?

The Bradis table is a four-digit mathematical table of values of sines, cosines, tangents and cotangents for angles from 0° to 90° with a step of 1 minute. It was developed by the Soviet mathematician Vladimir Bradis in 1921.

How to use the Bradis table?

Find the row with degrees and the column with minutes. At the intersection — the value of the function. If the angle contains minutes that are not multiples of 6, use the corrections from the last three columns of the table: for sine and tangent, add; for cosine and cotangent, subtract.

What are corrections in the Bradis table?

Corrections are values that must be added or subtracted from the table value if the angle is not a multiple of 6 minutes. They are indicated in the last columns of the table for 1′, 2′ and 3′. For sine and tangent, the correction is added; for cosine and cotangent, it is subtracted.

How do Bradis tables differ from a calculator?

Bradis tables provide values with an accuracy of four digits (0.0001). Modern calculators are more accurate. However, working with tables develops interpolation skills and understanding of trigonometric functions.

For which angles is the Bradis table used?

The Bradis table contains values for angles from 0° to 90°. For angles greater than 90°, reduction formulas are used to reduce them to the first quadrant.

How to find values for angles greater than 90°?

For angles greater than 90°, reduction formulas are applied. For example, sin 120° = sin (180° − 60°) = sin 60° = 0.8660; cos 150° = −cos 30° = −0.8660. Thus the angle is reduced to the first quadrant, and the value is taken from the Bradis table.

How accurate are the values in this table?

The values in the table are given with an accuracy of four decimal places (0.0001), which corresponds to the classic Bradis tables and is sufficient for most school and engineering problems. For higher accuracy, use the trigonometric calculator on this page.

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Compiled by: Alexey Pavlov, mathematics teacher.
Source: classic four-digit mathematical tables by V. M. Bradis (1921) in modern edition.
Date updated: 01.10.2026.