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Таблица Брадиса

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline &10^{\prime}&9^{\prime}&8^{\prime}&7^{\prime}&6^{\prime}&5^{\prime}&4^{\prime}&3^{\prime}&2^{\prime}&1^{\prime}&0^{\prime}&ctg\\ \hline &&&&&&&&&&&& \\ \hline tg&0^{\prime}&1^{\prime}&2^{\prime}&3^{\prime}&4^{\prime}&5^{\prime}&6^{\prime}&7^{\prime}&8^{\prime}&9^{\prime}&0^{\prime}&ctg \\ \hline \begin{array}{l}{81^{\circ}} \\ {00^{\prime}}\end{array}&6,314 &6,326 &6,338 &6,350 &6,362 &6,374 &6,386 &6,398 &6,410 &6,423 &6,435 &50^{\prime} \\ \hline 10^{\prime}&6.435 &6.447 &6,460 &6,472 &6.485 &6.497 &6.510 &6,522 &6.535 &6,548 &6,561 &40^{\circ} \\ \hline 20^{\prime}&6,561 &6,573 &6,586 &6.599 &6,612 &6,625 &6,638 &6.651 &6,665 &6,678 &6,691 &30^{\prime} \\ \hline 30^{\prime}&6,691 &6,704 &6,718 &6.731 &6.745 &6,758 &6,772 &6,786 &6,799 &6,813 &6,827 &20^{\prime} \\ \hline 40^{\prime}&6,827 &6,841 &6,855 &6,869 &6,883 &6.897 &6,911 &6,925 &6.940 &6.954 &6,968 &10^{\prime} \\ \hline 50^{\prime}&6,968 &6,983 &6,997 &7.012 &7,026 &7,041 &7,056 &7,071 &7,085 &7,100 &7,115 &\begin{array}{l}{8^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{l}{82^{\circ}} \\ {00^{\prime}}\end{array} &7,115 &7,130 &7,146 &7,161 &7,176 &7,191 &7,207 &7,222 &7,238 &7,253 &7,269 &50^{\prime} \\ \hline 10^{\prime}&7,269 &7,130 &7.146 &7,161 &7.176 &7,191 &7,207 &7,222 &7,238 &7,253 &7,269 &40^{\prime} \\ \hline 20^{\prime}&7,429 &7.445 &7,462 &7.478 &7.495 &7.511 &7.528 &7,545 &7.562 &7,579 &7,596 &30^{\prime} \\ \hline 30^{\prime}&7,596 &7.613 &7,630 &7,647 &7,665 &7.682 &7,700 &7,717 &7,735 &7,753 &7,770 &20^{\prime} \\ \hline 40^{\prime}&7,770 &7,788 &7,806 &7.824 &7.842 &7,861 &7.879 &7,897 &7,916 &7.934 &7,953 &10^{\prime} \\ \hline 50^{\prime}&7,953 &7,972 &7,991 &8,009 &8,028 &8,048 &8,067 &8.086 &8,105 &8,125 &8,144 &\begin{array}{c}{7^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline &&&&&&&&&&&& \\ \hline \begin{array}{l}{83^{\circ}} \\ {00^{\prime}}\end{array}&8,144 &8,164 &8,184 &8,204 &8,223 &8,243 &8,264 &8,284 &8,304 &8,324 &8,345 &50^{\prime} \\ \hline 10^{\prime}&8,345 &8.366 &8.184 &8,204 &8,223 &8,243 &8,264 &8,284 &8,304 &8,324 &8,345 &40^{\prime} \\ \hline 20^{\prime}&8,556 &8,577 &8,599 &8.621 &8.643 &8,665 &8,687 &8,709 &8,732 &8,754 &8,777 &30^{\prime} \\ \hline 30^{\prime}&8.777 &8.800 &8.823 &8,846 &8.869 &8,892 &8,915 &8.939 &8.962 &8,986 &9,010 &20^{\prime} \\ \hline 40^{\prime}&9,010 &9.034 &9,058 &9,082 &9,106 &9,131 &9.156 &9,180 &9,205 &9,230 &9,255 &10^{\prime} \\ \hline 50^{\prime}&9,255 &9,281 &9,306 &9.332 &9,357 &9,383 &9,409 &9,435 &9,461 &9,488 &9,514 &\begin{array}{c}{6^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{c}{84^{\circ}} \\ {0^{\prime}}\end{array}&9,514 &9,541 &9,568 &9,595 &9,622 &9,649 &9,677 &9,704 &9,732 &9,760 &9,788 &50^{\prime} \\ \hline 10^{\prime}&9,788 &9,816 &9,845 &9,873 &9,902 &9.931 &9,960 &9,989 &10,02 &10,05 &10,08 &40^{\prime} \\ \hline 20^{\prime}&10,08 &10,11 &10.14 &10,17 &10,20 &10.23 &10,26 &10.29 &10.32 &10,35 &10,39 &30^{\prime} \\ \hline 30^{\prime}&10,39 &10,42 &10.45 &10,48 &10.51 &10.55 &10,58 &10,61 &10,64 &10,68 &10,71 &20^{\prime} \\ \hline 40^{\prime}&10,71 &10,75 &10.78 &10.81 &10,85 &10,88 &10,92 &10.95 &10,99 &11,02 &11,06 &10^{\prime} \\ \hline 50^{\prime}&11.06 &11.10 &11,13 &11.17 &11,20 &11.24 &11,28 &11,32 &11,35 &11,39 &11,43 &\begin{array}{c}{5^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{l}{85^{\circ}} \\ {00^{\prime}}\end{array}&11,43 &11,47 &11,51 &11,55 &11,59 &11,62 &11,66 &11,70 &11,74 &11,79 &11,83 &50^{\prime} \\ \hline 10^{\prime}&11,83 &11,87 &11,91 &11,95 &11,99 &12,03 &12,08 &12,12 &12,16 &12,21 &12,25 &40^{\prime} \\ \hline 20^{\prime}&12,25 &12,29 &12.34 &12,38 &12,43 &12,47 &12,52 &12,57 &12,61 &12,66 &12,71 30^{\prime} \\ \hline 30^{\prime}&12.71 &12.75 &12.80 &12.85 &12.90 &12.95 &13,00 &13.05 &13.10 &13.15 &13,20 &20^{\prime} \\ \hline 40^{\prime}&13,20 &13,25 &13,30 &13,35 &13,40 &13,46 &13,51 &13,56 &13,62 &13,67 &13,73 &10^{\prime} \\ \hline 50^{\prime}&13,73 &13,78 &13,84 &13,89 &13,95 &14,01 &14,07 &14,12 &14,18 &14,24 &14,30 &\begin{array}{c}{4^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \end{array} \)

ОПРЕДЕЛЕНИЕ

Таблицы Bradis представляют собой наиболее полную коллекцию всех синусоидальных, косинусных, касательных, кокасательных и других значений. Эти таблицы очень точны, достигая четырех знаков после запятой, что позволяет использовать их как для решения школьных задач в алгебре, геометрии, физике, так и для расчета сложных технических расчетов.

Правила использования таблиц: таблицы дают значения синусов (косинусов) любого острого угла, содержащие целое число и десятые доли градуса, на пересечении линии, имеющей соответствующее количество градусов в заголовке слева и столбец в заголовке выше количества минут.

ВНИМАНИЕ, в данной статье таблица приведена в виде изображения, и годится для вычислений, если вам необходимо скопировать таблицу в текстовом виде, перейдите по ссылке.

Тригонометрические функции sin x и cos x аргумента в градусах

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline sin&0^{\prime}&6^{\prime}&12^{\prime}&18^{\prime}&24^{\prime}&30^{\prime}&36^{\prime}&42^{\prime}&48^{\prime}&54^{\prime}&60^{\prime}&cos&1^{\prime}&2^{\prime} &3^{\prime}\\ \hline &&&&&&&&&&&0.0000 &90^{\circ}&&& \\ \hline 0^{\circ}&0.0000&0017 &0035 &0052 &0070 &0087 &0105 &0122 &0140 &0157 &0175&89^{\circ}&3&6&9 \\ \hline 1^{\circ}&0175&0192 &0209 &0227 &0244 &0262 &0279 &0297 &0314 &0332 &0349&88^{\circ}&3&6&9 \\ \hline 2^{\circ}&0349&0366 &0384 &0401 &0419 &0436 &0454 &0471 &0488 &0506 &0523&87^{\circ}&3&6&9 \\ \hline 3^{\circ}&0523 &0541 &0558 &0576 &0593 &0610 &0628 &0645 &0663 &0680 &0698&86^{\circ}&3&6&9 \\ \hline 4^{\circ}&0698 &0715 &0732 &0750 &0767 &0785 &0802 &0819 &0837 &0854 &0.0872&85^{\circ}&3&6&9 \\ \hline &&&&&&&&&&&&&& \\ \hline 5^{\circ}&0.0872 &0889 &0906 &0924 &0941 &0958 &0976 &0993 &1011 &1028 &1045&84^{\circ}&3&6&9 \\ \hline 6^{\circ}&1045 &1063 &1080 &1097 &1115 &1132 &1149 &1167 &1184 &1201 &1219&83^{\circ}&3&6&9 \\ \hline 7^{\circ}&1219 &1236 &1253 &1271 &1288 &1305 &1323 &1340 &1357 &1374 &1392&82^{\circ}&3&6&9 \\ \hline 8^{\circ}&1392 &1409 &1426 &1444 &1461 &1478 &1495 &1513 &1530 &1547 &1564&81^{\circ}&3&6&9 \\ \hline 9^{\circ}&1564 &1582 &1599 &1616 &1633 &1650 &1668 &1685 &1702 &1719 &0.1736&80^{\circ}&3&6&9 \\ \hline &&&&&&&&&&&&&& \\ \hline 10^{\circ}&0.1736 &1754 &1771 &1788 &1805 &1822 &1840 &1857 &1874 &1891 &1908&79^{\circ}&3&6&9 \\ \hline 11^{\circ}&1908 &1925 &1942 &1959 &1977 &1994 &2011 &2028 &2045 &2062 &2079&78^{\circ}&3&6&9 \\ \hline 12^{\circ}&2079 &2096 &2113 &2130 &2147 &2164 &2181 &2198 &2215 &2233 &2250&77^{\circ}&3&6&9 \\ \hline 13^{\circ}&2250 &2267 &2284 &2300 &2317 &2334 &2351 &2368 &2385 &2402 &2419&76^{\circ}&3&6&8 \\ \hline 14^{\circ}&2419 &2436 &2453 &2470 &2487 &2504 &2521 &2538 &2554 &2571 &0.2588&75^{\circ}&3&6&8 \\ \hline &&&&&&&&&&&&&& \\ \hline 15^{\circ}&0.2588 &2605 &2622 &2639 &2656 &2672 &2689 &2706 &2723 &2740 &2756&74^{\circ}&3&6&8 \\ \hline 16^{\circ}&2756 &2773 &2790 &2807 &2823 &2840 &2857 &2874 &2890 &2907 &2924&73^{\circ}&3&6&8 \\ \hline 17^{\circ}&2942 &2940 &2957 &2974 &2990 &3007 &3024 &3040 &3057 &3074 &3090&72^{\circ}&3&6&8 \\ \hline 18^{\circ}&3090 &3107 &3123 &3140 &3156 &3173 &3190 &3206 &3223 &3239 &3256&71^{\circ}&3&6&8 \\ \hline 19^{\circ}&3256 &3272 &3289 &3305 &3322 &3338 &3355 &3371 &3387 &3404 &0.3420&70^{\circ}&3&5&8\\ \hline &&&&&&&&&&&&&& \\ \hline 20^{\circ}&0.3420 &3437 &3453 &3469 &3486 &3502 &3518 &3535 &3551 &3567 &3584&69^{\circ}&3&5&8 \\ \hline 21^{\circ}&3584 &3600 &3616 &3633 &3649 &3665 &3681 &3697 &3714 &3730 &3746&68^{\circ}&3&5&8 \\ \hline 22^{\circ}&3746 &3762 &3778 &3795 &3811 &3827 &3843 &3859 &3875 &3891 &3907&67^{\circ}&3&5&8 \\ \hline 23^{\circ}&3097 &3923 &3939 &3955 &3971 &3987 &4003 &4019 &4035 &4051 &4067&66^{\circ}&3&5&8 \\ \hline 24^{\circ}&4067 &4083 &4099 &4115 &4131 &4147 &4163 &4179 &4195 &4210 &0.4226&65^{\circ}&3&5&8 \\ \hline &&&&&&&&&&&&&& \\ \hline 25^{\circ}&0.4226 &4242 &4258 &4274 &4289 &4305 &4321 &4337 &4352 &4368 &4384&64^{\circ}&3&5&8 \\ \hline 26^{\circ}&4384 &4399 &4415 &4431 &4446 &4462 &4478 &4493 &4509 &4524 &4540&63^{\circ}&3&5&8 \\ \hline 27^{\circ}&4540 &4555 &4571 &4586 &4602 &4617 &4633 &4648 &4664 &4679 &4695&62^{\circ}&3&5&8 \\ \hline 28^{\circ}&4695 &4710 &4726 &4741 &4756 &4772 &4787 &4802 &4818 &4833 &4848&61^{\circ}&3&5&8 \\ \hline 29^{\circ}&4848 &4863 &4879 &4894 &4909 &4924 &4939 &4955 &4970 &4985 &0.5000&60^{\circ}&3&5&8 \\ \hline &&&&&&&&&&&&&& \\ \hline 30^{\circ}&0.5000 &5015 &5030 &5045 &5060 &5075 &5090 &5105 &5120 &5135 &5150&59^{\circ}&3&5&8 \\ \hline 31^{\circ}&5150 &5165 &5180 &5195 &5210 &5225 &5240 &5255 &5270 &5284 &5299&58^{\circ}&2&5&7 \\ \hline 32^{\circ}&5299 &5314 &5329 &5344 &5358 &5373 &5388 &5402 &5417 &5432 &5446&57^{\circ}&2&5&7 \\ \hline 33^{\circ}&5446 &5461 &5476 &5490 &5505 &5519 &5534 &5548 &5563 &5577 &5592&56^{\circ}&2&5&7 \\ \hline 34^{\circ}&5592 &5606 &5621 &5635 &5650 &5664 &5678 &5693 &5707 &5721 &0.5736&55^{\circ}&2&5&7 \\ \hline &&&&&&&&&&&&&& \\ \hline 35^{\circ}&0.5736 &5750 &5764 &5779 &5793 &5807 &5821 &5835 &5850 &5864 &0.5878&54^{\circ}&2&5&7 \\ \hline 36^{\circ}&5878 &5892 &5906 &5920 &5934 &5948 &5962 &5976 &5990 &6004 &6018&53^{\circ}&2&5&7 \\ \hline 37^{\circ}&6018 &6032 &6046 &6060 &6074 &6088 &6101 &6115 &6129 &6143 &6157&52^{\circ}&2&5&7 \\ \hline 38^{\circ}&6157 &6170 &6184 &6198 &6211 &6225 &6239 &6252 &6266 &6280 &6293&51^{\circ}&2&5&7 \\ \hline 39^{\circ}&6293 &6307 &6320 &6334 &6347 &6361 &6374 &6388 &6401 &6414 &50^{\circ}&2&5&7 \\ \hline &60^{\prime} &54^{\prime} &48^{\prime} &42^{\prime} &36^{\prime} &30^{\prime} &24^{\prime} &18^{\prime} &12^{\prime} &6^{\prime} &\theta^{\prime}&cos&1^{\prime}&2^{\prime}&3^{\prime} \\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline sin&0^{\prime}&6^{\prime}&12^{\prime}&18^{\prime}&24^{\prime}&30^{\prime}&36^{\prime}&42^{\prime}&48^{\prime}&54^{\prime}&60^{\prime}&cos&1^{\prime}&2^{\prime}&3^{\prime} \\ \hline 40^{\circ}&0.6428&6441&6455&6468&6481&6494&6508&6521&6534&6547&6561&49^{\circ}&2&4&7 \\ \hline 41^{\circ}&6561&6574&6587&6600&6613&6626&6639&6652&6665&6678&6691&48^{\circ}&2&4&8 \\ \hline 42^{\circ}&6691&6704&6717&6730&6743&6756&6769&6782&6794&6807&6820&47^{\circ}&2&4&6 \\ \hline 43^{\circ}&6820&6833&6845&6858&6871&6884&6896&8909&6921&6934&6947&46^{\circ}&2&4&6 \\ \hline 44^{\circ}&6947&6959&6972&6984&6997&7009&7022&7034&7046&7059&0.7071&45^{\circ}&2&4&6 \\ \hline &&&&&&&&&&&&&& \\ \hline 45^{\circ}&0.7071&7083&7096&7108&7120&7133&7145&7157&7169&7181&7193&44^{\circ}&2&4&7 \\ \hline 46^{\circ}&7193&7206&7218&7230&7242&7254&7266&7278&7290&7302&7314&43^{\circ}&2&4&7 \\ \hline 47^{\circ}&7314&7325&7337&7349&7361&7373&7385&7396&7408&7420&7431&42^{\circ}&2&4&7 \\ \hline 48^{\circ}&7431&7443&7455&7466&7478&7490&7501&7513&7524&7536&7547&41^{\circ}&2&4&7 \\ \hline 49^{\circ}&7547&7559&7570&7581&7593&7604&7615&7627&7638&7649&0.7660&40^{\circ}&2&4&7 \\ \hline &&&&&&&&&&&&&& \\ \hline 50^{\circ}&0.7660&7672&7683&7694&7705&7716&7727&7738&7749&7760&7771&39^{\circ}&2&4&6 \\ \hline 51^{\circ}&7771&7782&7793&7804&7815&7826&7837&7848&7859&7869&7880&38^{\circ}&2&4&5 \\ \hline 52^{\circ}&7880&7891&7902&7912&7923&7934&7944&7955&7965&7976&7986&37^{\circ}&2&4&5 \\ \hline 53^{\circ}&7986&7997&8007&8018&8028&8039&8049&8059&8070&8080&8090&36^{\circ}&2&3&5 \\ \hline 54^{\circ}&8090&8100&8111&8121&8131&8141&8151&8161&8171&8181&0.8192&35^{\circ}&2&3&5 \\ \hline &&&&&&&&&&&&&& \\ \hline 55^{\circ}&0.8192&8202&8211&8221&8231&8241&8251&8261&8271&8281&8290&34^{\circ}&2&3&5 \\ \hline 56^{\circ}&8290&8300&8310&8320&8329&8339&8348&8358&8368&8377&8387&33^{\circ}&2&3&5\\ \hline 57^{\circ}&8387&8396&8406&8415&8425&8434&8443&8453&8462&8471&8480&32^{\circ}&2&3&5 \\ \hline 58^{\circ}&8480&8490&8499&8508&8517&8526&8536&8545&8554&8563&8572&31^{\circ}&2&3&5 \\ \hline 59^{\circ}&8572&8581&8590&8599&8607&8616&8625&8634&8643&8652&0.8660&30^{\circ}&1&3&4 \\ \hline &&&&&&&&&&&&&& \\ \hline 60^{\circ}&0.8660&8669&8678&8686&8695&8704&8712&8721&8729&8738&8746&29^{\circ}&1&3&4 \\ \hline 61^{\circ}&8746&8755&8763&8771&8780&8788&8796&8805&8813&8821&8829&28^{\circ}&1&3&4 \\ \hline 62^{\circ}&8829&8838&8846&8854&8862&8870&8878&8886&8894&8902&8910&27^{\circ}&1&3&4 \\ \hline 63^{\circ}&8910&8918&8926&8934&8942&8949&8957&8965&8973&8980&8988&26^{\circ}&1&3&4 \\ \hline 64^{\circ}&8988&8996&9003&9011&9018&9026&9033&9041&9048&9056&0.9063&25^{\circ}&1&3&4 \\ \hline &&&&&&&&&&&&&& \\ \hline 65^{\circ}&0.9063&9070&9078&9085&9092&9100&9107&9114&9121&9128&9135&24^{\circ}&1&2&4 \\ \hline 66^{\circ}&9135&9143&9150&9157&9164&9171&9178&9184&9191&9198&9205&23^{\circ}&1&2&3 \\ \hline 67^{\circ}&9205&9212&9219&9225&9232&9239&9245&9252&9259&9256&9272&22^{\circ}&1&2&3 \\ \hline 68^{\circ}&9272&9278&9285&9291&9298&9304&9311&9317&9323&9330&9336&21^{\circ}&1&2&3 \\ \hline 69^{\circ}&9336&9342&9348&9354&9361&9367&9373&9379&9383&9391&0.9397&20^{\circ}&1&2&3 \\ \hline &&&&&&&&&&&&&& \\ \hline 70^{\circ}&9397&9403&9409&9415&9421&9426&9432&9438&9444&9449&0.9455&19^{\circ}&1&2&3 \\ \hline 71^{\circ}&9455&9461&9466&9472&9478&9483&9489&9494&9500&9505&9511&18^{\circ}&1&2&3 \\ \hline 72^{\circ}&9511&9516&9521&9527&9532&9537&9542&9548&9553&9558&9563&17^{\circ}&1&2&3 \\ \hline 73^{\circ}&9563&9568&9573&9578&9583&9588&9593&9598&9603&9608&9613&16^{\circ}&1&2&2\\ \hline 74^{\circ}&9613&9617&9622&9627&9632&9636&9641&9646&9650&9655&0.9659&15^{\circ}&1&2&2\\ \hline &&&&&&&&&&&&&& \\ \hline 75^{\circ}&9659&9664&9668&9673&9677&9681&9686&9690&9694&9699&9703&14^{\circ}&1&1&2 \\ \hline 76^{\circ}&9703&9707&9711&9715&9720&9724&9728&9732&9736&9740&9744&13^{\circ}&1&1&2 \\ \hline 77^{\circ}&9744&9748&9751&9755&9759&9763&9767&9770&9774&9778&9781&12^{\circ}&1&1& 2\\ \hline 78^{\circ}&9781&9785&9789&9792&9796&9799&9803&9806&9810&9813&9816&11^{\circ}&1&1&2 \\ \hline 79^{\circ}&9816&9820&9823&9826&9829&9833&9836&9839&9842&9845&0.9848&10^{\circ}&1&1&2 \\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline sin&0^{\prime}&6^{\prime}&12^{\prime}&18^{\prime}&24^{\prime}&30^{\prime}&36^{\prime}&42^{\prime}&48^{\prime}&54^{\prime}&60^{\prime}&&1^{\prime}&2^{\prime}&3^{\prime} \\ \hline &&&&&&&&&&&&&&& \\ \hline 80^{\circ}&0.9848&9851&9854&9857&9860&9863&9866&9869&9871&9874&9877&9^{\circ}&0&1&1 \\ \hline 81^{\circ}&9877&9880&9882&9885&9888&9890&9893&9895&9898&9900&9903&8^{\circ}&0&1&1\\ \hline 82^{\circ}&9903&9905&9907&9910&9912&9914&9917&9919&9921&9923&9925&7^{\circ}&0&1&1 \\ \hline 83^{\circ}&9925&9928&9930&9932&9934&9936&9938&9940&9942&9943&9945&6^{\circ}&0&1&1 \\ \hline 84^{\circ}&9945&9947&9949&9951&9952&9954&9956&9957&9959&9960&9962&50&0&1&1 \\ \hline &&&&&&&&&&&&&&& \\ \hline 85^{\circ}&9962&9963&9965d&9966&9968&9969&9971&9972&9973&9974&9976&4^{\circ}&0&0&1 \\ \hline 86^{\circ}&9976&9977&9978&9979&9980&9981&9982&9983&9984&9985&9986&3^{\circ}&0&0&0 \\ \hline 87^{\circ}&9986&9987&9988&9989&9990&9990&9991&9992&9993&9993&9994&2^{\circ}&0&0&0 \\ \hline 88^{\circ}&9994&9995&9995&9996&9996&9997&9997&9997&9998&9998&0.9998&1^{\circ}&0&0&0 \\ \hline 89^{\circ}&9998&9999&9999&9999&9999&1.0000&1.0000&1.0000&1.0000&1.0000&1.0000&0^{\circ}&0&0&0\\ \hline 90^{\circ}&1.0000&&&&&&&&&&&&&& \\ \hline \end{array} \)

Тригонометрические функции Брадиса tg x, ctg x аргумента в градусах

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline tg&0^{\prime}&6^{\prime}&12^{\prime}&18^{\prime}&24^{\prime}&30^{\prime}&36^{\prime}&42^{\prime}&48^{\prime}&54^{\prime}&60^{\prime}&ctg&1^{\prime}&2^{\prime}&3^{\prime}\\ \hline &&&&&&&&&&&0&90^{\circ}&&& \\ \hline 0^{\circ}&0,000&0017&0035&0052&0070&0087&0105&0122&0140&0157&0175&89^{\circ}&3&6&9 \\ \hline 1^{\circ}&0175&0192&0209&0227&0244&0262&0279&0297&0314&0332&0349&88^{\circ}&3&6&9 \\ \hline 2^{\circ}&0349&0367&0384&0402&0419&0437&0454&0472&0489&0507&0524&87^{\circ}&3&6&9 \\ \hline 3^{\circ}&0524&0542&0559&0577&0594&0612&0629&0647&0664&0682&0699&86^{\circ}&3&6&9 \\ \hline 4^{\circ}&0699&0717&0734&0752&0769&0787&0805&0822&0840&0857&0.0875&85^{\circ}&3&6& 9\\ \hline &&&&&&&&&&&&&& \\ \hline 5^{\circ}&0,0875&0892&0910&0928&0945&0963&0981&0998&1016&1033&1051&84^{\circ}&3&6&9 \\ \hline 6^{\circ}&1051&1069&1086&1104&1122&1139&1157&1175&1192&1210&1228&83^{\circ}&3&6&9 \\ \hline 7^{\circ}&1228&1246&1263&1281&1299&1317&1334&1352&1370&1388&1405&82^{\circ}&3&6&9 \\ \hline 8^{\circ}&1405&1423&1441&1459&1477&1495&1512&1530&1548&1566&1584&81^{\circ}&3&6&9 \\ \hline 9^{\circ}&1584&1602&1620&1638&1655&1673&1691&1709&1727&1745&0.1763&80^{\circ}&3&6&9 \\ \hline &&&&&&&&&&&&&& \\ \hline 10^{\circ}&0,1763&1781&1799&1817&1835&1853&1871&1890&1908&1926&1944&79^{\circ}&3&6&9 \\ \hline 11^{\circ}&1944&1962&1980&1998&2016&2035&2053&2071&2089&2107&2126&78^{\circ}&3&6&9 \\ \hline 12^{\circ}&2126&2144&2162&2180&2199&2217&2235&2254&2272&2290&2309&77^{\circ}&3&6&9 \\ \hline 13^{\circ}&2309&2327&2345&2364&2382&2401&2419&2438&2456&2475&2493&76^{\circ}&3&6&9 \\ \hline 14^{\circ}&2493&2512&2530&2549&2568&2586&2605&2623&2642&2661&0.2679&75^{\circ}&3&6&9\\ \hline &&&&&&&&&&&&&& \\ \hline 15^{\circ}&0,2679&2698&2717&2736&2754&2773&2792&2811&2830&2849&2867&74^{\circ}&3&6&9 \\ \hline 16^{\circ}&2867&2886&2905&2924&2943&2962&2981&3000&3019&3038&3057&73^{\circ}&3&6&9 \\ \hline 17^{\circ}&3057&3076&3096&3115&3134&3153&3172&3191&3211&3230&3249&72^{\circ}&3&6&10 \\ \hline 18^{\circ}&3249&3269&3288&3307&3327&3346&3365&3385&3404&3424&3443&71^{\circ}&3&6&10 \\ \hline 19^{\circ}&3443&3463&3482&3502&3522&3541&3561&3581&3600&3620&0,3640&70^{\circ}&3&7&10 \\ \hline &&&&&&&&&&&&&& \\ \hline 20^{\circ}&0.3640&3659&3679&3699&3719&3739&3759&3779&3799&3819&3839&69^{\circ}&3&7&10 \\ \hline 21^{\circ}&3839&3859&3879&3899&3919&3939&3959&3979&4000&4020&4040&68^{\circ}&3&7&10 \\ \hline 22^{\circ}&4040&4061&4081&4101&4122&4142&4163&4183&4204&4224&4245&67^{\circ}&3&7&10 \\ \hline 23^{\circ}&4245&4265&4286&4307&4327&4348&4369&4390&4411&4431&4452&66^{\circ}&3&7&10 \\ \hline 24^{\circ}&4452&4473&4494&4515&4536&4557&4578&4599&4621&4642&0.4663&65^{\circ}&3&7&11 \\ \hline &&&&&&&&&&&&&& \\ \hline 25^{\circ}&0,4663&4684&4706&4727&4748&4770&4791&4813&4834&4856&4877&64^{\circ}&4&7&11 \\ \hline 26^{\circ}&4877&4899&4921&4942&4964&4986&5008&5029&5051&5073&5095&63^{\circ}&4&7&11 \\ \hline 27^{\circ}&5095&5117&5139&5161&5184&5206&5228&5250&5272&5295&5317&62^{\circ}&4&7&11 \\ \hline 28^{\circ}&5317&5340&5362&5384&5407&5430&5452&5475&5498&5520&5543&61^{\circ}&4&8&11 \\ \hline 29^{\circ}&5543&5566&5589&5612&5635&5658&5681&5704&5727&5750&0.5774&60^{\circ}&4&8& 12\\ \hline &&&&&&&&&&&&&& \\ \hline 30^{\circ}&0,5774&5797&5820&5844&5867&5890&5914&5938&5961&5985&6009&59^{\circ}&4&8&12 \\ \hline 31^{\circ}&6009&6032&6056&6080&6104&6128&6152&6176&6200&6224&6249&58^{\circ}&4&8&12 \\ \hline 32^{\circ}&6249&6273&6297&6322&6346&6371&6395&6420&6445&6469&6494&57^{\circ}&4&8&12 \\ \hline 33^{\circ}&6494&6519&6544&6569&6594&6619&6644&6669&6694&6720&6745&56^{\circ}&4&8&13 \\ \hline 34^{\circ}&6745&6771&6796&6822&6847&6873&6899&6924&6950&6976&0.7002&55^{\circ}&4&9&13 \\ \hline &&&&&&&&&&&&&& \\ \hline 35^{\circ}&0,7002&7028&7054&7080&7107&7133&7159&7186&7212&7239&7265&54^{\circ}&4&8& 13\\ \hline 36^{\circ}&7265&7292&7319&7346&7373&7400&7427&7454&7481&7508&7536&53^{\circ}&5&9&14 \\ \hline 37^{\circ}&7536&7563&7590&7618&7646&7673&7701&7729&7757&7785&7813&52^{\circ}&5&9&14 \\ \hline 38^{\circ}&7813&7841&7869&7898&7926&7954&7983&8012&8040&8069&8098&51^{\circ}&5&9&14 \\ \hline 39^{\circ}&8098&8127&8156&8185&8214&8243&8273&8302&8332&8361&0,8391&50^{\circ}&5&10&15 \\ \hline &60^{\prime}&54^{\prime}&48^{\prime}&42^{\prime}&36^{\prime}&30^{\prime}&24^{\prime}&18^{\prime}&12^{\prime}&6^{\prime}&0^{\prime}&ctg&1^{\prime}&2^{\prime}&3^{\prime} \\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline tg&0^{\prime}&6^{\prime}&12^{\prime}&18^{\prime}&24^{\prime}&30^{\prime}&36^{\prime}&42^{\prime}&48^{\prime}&54^{\prime}&60^{\prime}&ctg&1^{\prime}&2^{\prime}&3^{\prime} \\ \hline &&&&&&&&&&&&&& \\ \hline 40^{\circ}&0.8391&8421&8451&8481&8511&8541&8571&8601&8632&8662&0.8693&49^{\circ}&5&10&15 \\ \hline 41^{\circ}&8693&8724&8754&8785&8816&8847&8878&8910&8941&8972&9004&48^{\circ}&5&10&16 \\ \hline 42^{\circ}&9004&9036&9067&9099&9131&9195&9228&9260&9293&9325&47^{\circ}&6&11&16 \\ \hline 43^{\circ}&9325&9358&9391&9424&9457&9490&9523&9556&9590&9623&0.9657&46^{\circ}&6&11&17 \\ \hline 44^{\circ}&9657&9691&9725&9759&9793&9827&9861&9896&9930&9965&1.0000&45^{\circ}&6&11&17 \\ \hline &&&&&&&&&&&&&& \\ \hline 45^{\circ}&1,0000&0035&0070&0105&0141&0176&0212&0247&0283&0319&0355&44^{\circ}&6&12&18 \\ \hline 46^{\circ}&0355&0392&0428&0464&0501&0538&0575&0612&0649&0686&0724&43^{\circ}&6&12&18 \\ \hline 47^{\circ}&0724&0761&0799&0837&0875&0913&0951&0990&1028&1067&1106&42^{\circ}&6&13&19 \\ \hline 48^{\circ}&1106&1145&1184&1224&1263&1303&1343&1383&1423&1463&1504&41^{\circ}&7&13&20 \\ \hline 49^{\circ}&1504&1544&1585&1626&1667&1708&1750&1792&1833&1875&1.1918&40^{\circ}&7&14&21 \\ \hline &&&&&&&&&&&&&& \\ \hline 50^{\circ}&1,1918&1960&2002&2045&2088&2131&2174&2218&2261&2305&2349&39^{\circ}&7&14&22 \\ \hline 51^{\circ}&2349&2393&2437&2482&2527&2572&2617&2662&2708&2753&2799&38^{\circ}&8&15&23 \\ \hline 52^{\circ}&2799&2846&2892&2938&2985&3032&3079&3127&3175&3222&3270&37^{\circ}&8&16&24 \\ \hline 53^{\circ}&3270&3319&3367&3416&3465&3514&3564&3613&3663&3713&3764&36^{\circ}&8&16&25 \\ \hline 54^{\circ}&3764&3814&3865&3916&3968&4019&4071&4124&4176&4229&1.4281&35^{\circ}&9&17&26 \\ \hline &&&&&&&&&&&&&& \\ \hline 55^{\circ}&1,4281&4335&4388&4442&4496&4550&4605&4659&4715&4770&4826&34^{\circ}&9&18&27 \\ \hline 56^{\circ}&4826&4882&4938&4994&5051&5108&5166&5224&5282&5340&5399&33^{\circ}&10&19&29 \\ \hline 57^{\circ}&5399&5458&5517&5577&5637&5697&5757&5818&5880&5941&6003&32^{\circ}&10&20&30 \\ \hline 58^{\circ}&6003&6066&6128&6191&6255&6319&6383&6447&6512&6577&6643&31^{\circ}&11&21&32 \\ \hline 59^{\circ}&6643&6709&6775&6842&6909&6977&7045&7113&7182&7251&1.7321&30^{\circ}&11&23&24 \\ \hline &&&&&&&&&&&&&& \\ \hline 60^{\circ}&1,732&1,739&1.746&1,753&1,760&1,767&1,775&1,782&1,789&1.797&1,804&29^{\circ}&1&2&4 \\ \hline 61^{\circ}&1,804&1,811&1,819&1,827&1.834&1,842&1,849&1,857&1,865&1,873&1,881&28^{\circ}&1&2&4 \\ \hline 62^{\circ}&1,881&1.889&1,897&1,905&1,913&1,921&1,929&1.937&1,946&1,954&1,963&27^{\circ}&1&3&4 \\ \hline 63^{\circ}&1,963&1,971&1,980&1,988&1.997&2,006&2,014&2,023&2,032&2,041&2,05&26^{\circ}&1&3&4 \\ \hline 64^{\circ}&2,050&2,059&2,069&2,078&2.087&2,097&2,106&2,116&2,125&2.135&2,145&25^{\circ}&2&3&5 \\ \hline &&&&&&&&&&&&&& \\ \hline 65^{\circ}&2.145&2,154&2.164&2,174&2,184&2,194&2,204&2,215&2,225&2,236&2.246&24^{\circ}&2&3&5 \\ \hline 66^{\circ}&2,246&2,257&2,267&2,278&2,289&2.3&2,311&2,322&2.333&2.344&2,356&23^{\circ}&2&4&5 \\ \hline 67^{\circ}&2.356&2,367&2,379&2,391&2,402&2,414&2,426&2,438&2,450&2,463&2,475&22^{\circ}&2&4&6 \\ \hline 68^{\circ}&2,475&2,488&2,5&2,513&2,526&2,539&2,552&2,565&2,578&2,592&2,605&21^{\circ}&2&4&6 \\ \hline 69^{\circ}&2,605&2,619&2,633&2.646&2,66&2,675&2,689&2,703&2,718&2,733&2,747&20^{\circ}&2&5&7 \\ \hline &&&&&&&&&&&&&& \\ \hline 70^{\circ}&2,747&2,762&2,778&2.793&2,808&2,824&2,840&2,856&2,872&2,888&2,904&19^{\circ}&3&5&8 \\ \hline 71^{\circ}&2,904&2,921&2,937&2,954&2,971&2.989&3,006&3,024&3,042&3,06&3,078&18^{\circ}&3&6&9 \\ \hline 72^{\circ}&3,078&3.096&3,115&3,133&3.152&3,172&3,191&3,211&3,230&3,251&3,271&17^{\circ}&3&6&10 \\ \hline 73^{\circ}&3,271&3.291&3.312&3.333&3,354&3,376&&&&&&16^{\circ}&3&7&10 \\ \hline &&&&&&&3,398&3,42&3,442&3.465&3,487&&4&7&11 \\ \hline 74^{\circ}&3,487&3.511&3,534&3,558&3,582&3,606&&&&&&15^{\circ}&4&8&13 \\ \hline &&&&&&&3,630&3,655&3,681&3,706&3,732&&4&8&13 \\ \hline 75^{\circ}&3,732&3,758&3,785&3,812&3,839&3,867&&&&&&14^{\circ}&4&9&13 \\ \hline &&&&&&&3.895&3,923&3,952&3,981&4,011&&5&10&14 \\ \hline tg&60^{\prime}&54^{\prime}&48^{\prime}&42^{\prime}&36^{\prime}&30^{\prime}&24^{\prime}&18^{\prime}&12^{\prime}&6^{\prime}&0^{\prime}&ctg&1^{\prime}&2^{\prime}&3^{\prime} \\ \hline \end{array} \)

Таблица Брадиса - касательные углов, близкие к 90 °, котангенсы малых углов

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline tg&0^{\prime}&1^{\prime}&2^{\prime}&3^{\prime}&4^{\prime}&5^{\prime}&6^{\prime}&7^{\prime}&8^{\prime}&9^{\prime}&10^{\prime}&ctg\\ \hline \begin{array}{c}{76^{\circ}} \\ {00^{\prime}}\end{array}&4,011&4,016&4,021&4,026&4,031&4,036&4.041&4,046&4,051&4,056&4,061&50^{\prime}\\ \hline &&&&&&&&&&&& \\ \hline 10^{\prime}&4,061&4,066&4,071&4,076&4,082&4,087&4.092&4,097&4,102&4.107&4,113&40^{\prime} \\ \hline 20^{\prime}&4.113&4,118&4.123&4.128&4,134&4.139&4,144&4.149&4.155&4,160&4.165&30^{\prime} \\ \hline 30^{\prime}&4.165&4.171&4,176&4,181&4.187&4.192&4.198&4.203&4.208&4.214&4.219&20^{\prime}\\ \hline 40^{\prime}&4.219&4,225&4,230&4,236&4,241&4.247&4,252&4,258&4,264&4,269&4.275&10^{\prime} \\ \hline 50^{\prime}&4,275&4,280&4,286&4,292&4,297&4,303&4,309&4,314&4,320&4,326&4.331&13^{\circ}\\ \hline &&&&&&&&&&&& \\ \hline \begin{array}{l}{77^{\circ}} \\ {00^{\prime}}\end{array} &4,331&4.337&4,343&4.349&4,355&4,360&4,366&4,372&4,378&4,384&4,390&50^{\prime} \\ \hline 10^{\prime}&4,390&4,396&4,402&4,407&4,413&4,419&4,425&4,431&4,437&4,443&4,449&40^{\prime} \\ \hline 20^{\prime}&4.449&4.455&4,462&4,468&4.474&4,480&4,486&4,492&4,498&4,505&4,511&30^{\prime} \\ \hline 30^{\prime}&4,511&4,517&4.523&4,529&4,536&4,542&4.548&4,555&4,561&4,567&4,574&20^{\prime} \\ \hline 40^{\prime}&4.574&4,580&4.586&4.593&4,599&4,606&4,612&4,619&4,625&4,632&4,638&10^{\prime} \\ \hline 50^{\prime}&4,638&4,645&4,651&4,658&4,665&4,671&4,678&4,685&4,691&4,698&4,705&\begin{array}{c}{12^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline &&&&&&&&&&&& \\ \hline \begin{array}{l}{78^{\circ}} \\ {00^{\prime}}\end{array}&4,705&4,711&4,718&4,725&4,732&4,739&4,745&4,752&4,759&4,766&4,773&50^{\prime} \\ \hline 10^{\prime}&4,773&4,780&4,787&4.794&4,801&4,808&4.815&4,822&4,829&4,836&4,843&40^{\prime} \\ \hline 20^{\prime}&4,843&4,850&4.857&4,864&4,872&4,879&4.886&4,893&4,901&4,908&4,915&30^{\prime} \\ \hline 30^{\prime}&4,915&4,922&4.930&4,937&4,945&4,952&4,959&4,967&4,974&4,982&4,989&20^{\prime} \\ \hline 40^{\prime}&4,989&4.997&5,005&5.012&5,020&5,027&5.035&5,043&5,050&5,058&5,066&10^{\prime} \\ \hline 50^{\prime}&5.066&5.074&5,081&5,089&5,097&5.105&5,113&5,121&5,129&5.137&5,145&11^{\circ}\\ \hline \begin{array}{c}{79^{\circ}} \\ {0^{\prime}}\end{array} &&&&&&&&&&&& \\ \hline 10^{\prime}&5,226&5,234&5,242&5,250&5,259&5,267&5.276&5,284&5,292&5,301&5,309&40^{\prime} \\ \hline 20^{\prime}&5,309&5.318&5,326&5.335&5.343&5,352&5.361&5,369&5,378&5,387&5,396&30^{\prime} \\ \hline 30^{\prime}&5.396&5,404&5,413&5,422&5,431&5,440&5,458&5.466&5,475&5,485&20^{\prime} \\ \hline 40^{\prime}&5.485&5.494&5.503&5,512&5,521&5,530&5,539&5,549&5,558&5.567&5,576&10^{\prime} \\ \hline 50^{\prime}&5,576&5,586&5.595&5,605&5,614&5,623&5.633&5,642&5.652&5,662&5,671&10^{\circ}\\ \hline \begin{array}{l}{80^{\circ}} \\ {00^{\prime}}\end{array}&5,671&5,681&5,691&5,700&5,710&5,720&5,730&5,740&5,749&5,759&5,769&50^{\prime} \\ \hline 10^{\prime}&5.769&5,779&5,789&5,799&5,810&5,820&5,830&5,840&5,850&5,861&5,871&40^{\prime} \\ \hline 20^{\prime}&5,871&5,881&5,892&5,902&5,912&5,923&5,933&5.944&5,954&5.965&5,976&30^{\prime} \\ \hline 30^{\prime}&5,976&5,986&5.997&6,008&6.019&6,030&6,041&6,051&6,062&6.073&6,084&20^{\prime} \\ \hline 40^{\prime}&6.084&6,096&6.107&6.118&6,129&6.140&6.152&6,163&6.174&6.186&6,197&10^{\prime} \\ \hline 50^{\prime}&6,197&6.209&6.220&6,232&6.243&6,255&6,267&6,278&6,290&6,302&6.314&\begin{array}{l}{9^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline tg&0^{\prime}&1^{\prime}&2^{\prime}&3^{\prime}&4^{\prime}&5^{\prime}&6^{\prime}&7^{\prime}&8^{\prime}&9^{\prime}&0^{\prime}&ctg \\ \hline \begin{array}{l}{81^{\circ}} \\ {00^{\prime}}\end{array}&6,314 &6,326 &6,338 &6,350 &6,362 &6,374 &6,386 &6,398 &6,410 &6,423 &6,435 &50^{\prime} \\ \hline 10^{\prime}&6.435 &6.447 &6,460 &6,472 &6.485 &6.497 &6.510 &6,522 &6.535 &6,548 &6,561 &40^{\circ} \\ \hline 20^{\prime}&6,561 &6,573 &6,586 &6.599 &6,612 &6,625 &6,638 &6.651 &6,665 &6,678 &6,691 &30^{\prime} \\ \hline 30^{\prime}&6,691 &6,704 &6,718 &6.731 &6.745 &6,758 &6,772 &6,786 &6,799 &6,813 &6,827 &20^{\prime} \\ \hline 40^{\prime}&6,827 &6,841 &6,855 &6,869 &6,883 &6.897 &6,911 &6,925 &6.940 &6.954 &6,968 &10^{\prime} \\ \hline 50^{\prime}&6,968 &6,983 &6,997 &7.012 &7,026 &7,041 &7,056 &7,071 &7,085 &7,100 &7,115 &\begin{array}{l}{8^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{l}{82^{\circ}} \\ {00^{\prime}}\end{array} &7,115 &7,130 &7,146 &7,161 &7,176 &7,191 &7,207 &7,222 &7,238 &7,253 &7,269 &50^{\prime} \\ \hline 10^{\prime}&7,269 &7,130 &7.146 &7,161 &7.176 &7,191 &7,207 &7,222 &7,238 &7,253 &7,269 &40^{\prime} \\ \hline 20^{\prime}&7,429 &7.445 &7,462 &7.478 &7.495 &7.511 &7.528 &7,545 &7.562 &7,579 &7,596 &30^{\prime} \\ \hline 30^{\prime}&7,596 &7.613 &7,630 &7,647 &7,665 &7.682 &7,700 &7,717 &7,735 &7,753 &7,770 &20^{\prime} \\ \hline 40^{\prime}&7,770 &7,788 &7,806 &7.824 &7.842 &7,861 &7.879 &7,897 &7,916 &7.934 &7,953 &10^{\prime} \\ \hline 50^{\prime}&7,953 &7,972 &7,991 &8,009 &8,028 &8,048 &8,067 &8.086 &8,105 &8,125 &8,144 &\begin{array}{c}{7^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline &&&&&&&&&&&& \\ \hline \begin{array}{l}{83^{\circ}} \\ {00^{\prime}}\end{array}&8,144 &8,164 &8,184 &8,204 &8,223 &8,243 &8,264 &8,284 &8,304 &8,324 &8,345 &50^{\prime} \\ \hline 10^{\prime}&8,345 &8.366 &8.184 &8,204 &8,223 &8,243 &8,264 &8,284 &8,304 &8,324 &8,345 &40^{\prime} \\ \hline 20^{\prime}&8,556 &8,577 &8,599 &8.621 &8.643 &8,665 &8,687 &8,709 &8,732 &8,754 &8,777 &30^{\prime} \\ \hline 30^{\prime}&8.777 &8.800 &8.823 &8,846 &8.869 &8,892 &8,915 &8.939 &8.962 &8,986 &9,010 &20^{\prime} \\ \hline 40^{\prime}&9,010 &9.034 &9,058 &9,082 &9,106 &9,131 &9.156 &9,180 &9,205 &9,230 &9,255 &10^{\prime} \\ \hline 50^{\prime}&9,255 &9,281 &9,306 &9.332 &9,357 &9,383 &9,409 &9,435 &9,461 &9,488 &9,514 &\begin{array}{c}{6^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{c}{84^{\circ}} \\ {0^{\prime}}\end{array}&9,514 &9,541 &9,568 &9,595 &9,622 &9,649 &9,677 &9,704 &9,732 &9,760 &9,788 &50^{\prime} \\ \hline 10^{\prime}&9,788 &9,816 &9,845 &9,873 &9,902 &9.931 &9,960 &9,989 &10,02 &10,05 &10,08 &40^{\prime} \\ \hline 20^{\prime}&10,08 &10,11 &10.14 &10,17 &10,20 &10.23 &10,26 &10.29 &10.32 &10,35 &10,39 &30^{\prime} \\ \hline 30^{\prime}&10,39 &10,42 &10.45 &10,48 &10.51 &10.55 &10,58 &10,61 &10,64 &10,68 &10,71 &20^{\prime} \\ \hline 40^{\prime}&10,71 &10,75 &10.78 &10.81 &10,85 &10,88 &10,92 &10.95 &10,99 &11,02 &11,06 &10^{\prime} \\ \hline 50^{\prime}&11.06 &11.10 &11,13 &11.17 &11,20 &11.24 &11,28 &11,32 &11,35 &11,39 &11,43 &\begin{array}{c}{5^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{l}{85^{\circ}} \\ {00^{\prime}}\end{array}&11,43 &11,47 &11,51 &11,55 &11,59 &11,62 &11,66 &11,70 &11,74 &11,79 &11,83 &50^{\prime} \\ \hline 10^{\prime}&11,83 &11,87 &11,91 &11,95 &11,99 &12,03 &12,08 &12,12 &12,16 &12,21 &12,25 &40^{\prime} \\ \hline 20^{\prime}&12,25 &12,29 &12.34 &12,38 &12,43 &12,47 &12,52 &12,57 &12,61 &12,66 &12,71 30^{\prime} \\ \hline 30^{\prime}&12.71 &12.75 &12.80 &12.85 &12.90 &12.95 &13,00 &13.05 &13.10 &13.15 &13,20 &20^{\prime} \\ \hline 40^{\prime}&13,20 &13,25 &13,30 &13,35 &13,40 &13,46 &13,51 &13,56 &13,62 &13,67 &13,73 &10^{\prime} \\ \hline 50^{\prime}&13,73 &13,78 &13,84 &13,89 &13,95 &14,01 &14,07 &14,12 &14,18 &14,24 &14,30 &\begin{array}{c}{4^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \begin{array}{c}{86^{\circ}} \\ {00^{\prime}}\end{array}&14,30&14,36&14,42&14,48&14,54&14,61&14,67&14,73&14,80&14,86&14,92&50^{\prime} \\ \hline 10^{\prime}&14,92&14,99&15,06&15.12&15.19&15,26&15,33&15.39&15,46&15,53&15,60&40^{\prime} \\ \hline 20^{\prime}&15,60&15,68&15.75&15,82&15.89&15,97&16,04&16,12&16,20&16,27&16,35&30^{\prime} \\ \hline 30^{\prime}&16,35&16.43&16,51&16.59&16.67&16.75&16,83&16,92&17,00&17,08&17,17&20^{\prime} \\ \hline 40^{\prime}&17.17&17,26&17,34&17.43&17.52&17,61&17,70&17,79&17,89&17,98&18,07&10^{\prime} \\ \hline 50^{\prime}&18,07&18,17&18,27&18,37&18,46&18,56&18,67&18,77&18,87&18,98&19,08&\begin{array}{l}{3^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline &&&&&&&&&&&& \\ \hline \begin{array}{l}{87^{\circ}} \\ {00^{\prime}}\end{array} &19,08&19,19&19,30&19,41&19,52&19,63&19,74&19,85&19,97&20,09&20,21&50^{\prime} \\ \hline 10^{\prime}&20,21&20,33&20,45&20,57&20,69&20,82&20,95&21,07&21,20&21.34&21,47&40^{\prime} \\ \hline 20^{\prime}&21,47&21,61&21.74&21,88&22.02&22,16&22,31&22,45&22,60&22,75&22,90&30^{\prime} \\ \hline 30^{\prime}&22,90&23,06&23,21&23,37&23,53&23,69&23,86&24,03&24,20&24,37&24,54&20^{\prime} \\ \hline 40^{\prime}&24,54&24,72&24,90&25.08&25.26&25,45&25,64&25.83&26,03&26,23&26,43&10^{\prime} \\ \hline 50^{\prime}&26,43&26,64&26,84&27,06&27,27&27,49&27,71&27.94&28,17&28,40&28,64&\begin{array}{c}{2^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline \begin{array}{l}{88^{\circ}} \\ {00^{\prime}}\end{array} &28,64&28,88&29,12&29,37&29,62&29,88&30,14&30,41&30,68&30,96&31,24&50^{\prime} \\ \hline 10^{\prime}&31,24&31,53&31,82&32,12&32,42&32,73&33,05&33.37&33,69&34,03&34,37&40^{\prime} \\ \hline 20^{\prime}&34.37&34,72&35,07&35.43&35,80&36,18&36.56&36,96&37,36&37.77&38,19&30^{\prime} \\ \hline 30^{\prime}&38.19&38,62&39.06&39,51&39.97&40.44&40,92&41,41&41,92&42,43&42,96&20^{\prime} \\ \hline 40^{\prime}&42,96&43,51&44,07&44,64&45,23&45,83&46,45&47,09&47,74&48,41&49,10&10^{\prime} \\ \hline 50^{\prime}&49,10&49,82&50,55&51,30&52,08&52,88&53,71&54,56&55,44&56,35&57,29&\begin{array}{c}{1^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline &&&&&&&&&&&& \\ \hline \begin{array}{l}{89^{\circ}} \\ {00^{\prime}}\end{array} &57,29&58,26&59,27&60,31&61,38&62,50&63,66&64,86&66,11&67,40&68,75&50^{\prime} \\ \hline 10^{\prime}&68.75&70,15&71,62&73.14&74,73&76,39&78,13&79,94&81,85&83,84&85,94&40^{\prime} \\ \hline 20^{\prime}&85,94&88,14&90,46&92,91&95,49&98,22&101,1&104,2&107,4&110,9&114,6&30^{\prime} \\ \hline 30^{\prime}&114,6&118,5&122,8&127,3&132,2&137.5&143,2&149,5&156,3&163.7&I 71,9&20^{\prime} \\ \hline 40^{\prime}&171,9&180,9&191,0&202,2&214,9&229,2&245,6&264,4&286.5&312,5&343,8&10^{\prime} \\ \hline 50^{\prime}&343,8&382,0&429,7&491,1&573.0&687,5&859,4&1146,0&1719,0&3438,0&\begin{array}{c}{0^{\circ}} \\ {00^{\prime}}\end{array} \\ \hline tg&10^{\prime}&9^{\prime}&8^{\prime}&7^{\prime}&6^{\prime}&5^{\prime}&4^{\prime}&3^{\prime}&2^{\prime}&1^{\prime}&0^{\prime}&ctg \\ \hline \end{array} \)

Тригонометрические функции аргумента в радианах

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x&sin x&cos x&tg x&X&sin x&cos x&tg x&X&sin x&cos x&tg x\\ \hline 0,00&0,0000&1,0000&0,0000&1,05&0,8674&0,4976&1,7433&2,10&0,8632&-0.5048&-1,7098\\ \hline 0,01&0100&1,0000&0100&1,06&8724&4889&7844&2,11&8581&5135&6713\\ \hline 0,02&0200&0.9998&0200&1,07&8772&4801&8270&2,12&8529&5220&6340\\ \hline 0,03&0300&9996&0300&1,08&8820&4713&8712&2,13&8477&5305&5979\\ \hline 0,04&0400&9992&0400&1,09&8866&4625&9171&2,14&8423&5390&5629\\ \hline 0,05&0,0500&0,9988&0,0500&1,10&0.8912&0,4536&1,9648&2,15&0,8369&-0,5474&-1,5290\\ \hline 0,06&0600&9982&0601&1,11&8957&4447&2,0143&2,16&8314&5557&4961\\ \hline 0,07&0699&9976&0701&1,12&9001&4357&0660&2,17&8258&5640&4642\\ \hline 0,08&0799&9968&0802&1,13&9044&4267&1198&2,18&8201&5722&4332\\ \hline 0,09&0899&9960&0902&1,14&9086&4176&1759&2,19&8143&5804&4031\\ \hline &&&&&&&&&&&\\ \hline 0,10&0,0998&0,9950&0,1003&1,15&0,9128&0,4085&2,2345&2,20&0,8085&-0,5885&-1,3738\\ \hline 0,11&1098&9940&1105&1,16&9168&3993&2958&2,21&8026&5966&3453\\ \hline 0,12&1197&9928&1205&1,17&9208&3902&3600&2,22&7966&6046&3176\\ \hline 0,13&1296&9916&1307&1,18&9246&3809&4273&2,23&7905&6125&2906\\ \hline 0,14&1395&9902&1409&1,19&9284&3717&4979&2,24&7843&6204&2643\\ \hline 0,15&0,1494&0,9888&0.1511&1,20&0.932&0,3624&2,572&2,25&0.7781&-0,6282&-1,2386\\ \hline 0,16&1593&9872&1614&1,21&9356&3530&650&2,26&7717&6359&2136\\ \hline 0,17&1692&9856&1717&1,22&9391&3436&733&2,27&7654&6436&1892\\ \hline 0,18&1790&9838&1820&1,23&9425&3342&820&2,28&7589&6512&1653\\ \hline 0,19&1889&9820&1923&1,24&9458&3248&912&2,29&7523&6588&1420\\ \hline &&&&&&&&&&&\\ \hline 0,20&0.1987&0,9801&0,2027&1,25&0,9490&0,3153&3,010&2,30&0.7457&-0.6663&-1,1192\\ \hline 0,21&2085&9780&2131&1,26&9521&3058&113&2,31&7390&6737&0969\\ \hline 0,22&2182&9759&2236&1,27&9551&2963&224&2,32&7322&6811&0751\\ \hline 0,23&2280&9737&2341&1,28&9580&2867&341&2,33&7254&6883&0538\\ \hline 0,24&2377&9713&2447&1,29&9608&2771&467&2,34&7185&6956&0329\\ \hline 0,25&0.2474&0.9689&0,2553&1,30&0,9636&0,2675&3.602&2,35&0,7115&-0,7027&-1,0125\\ \hline 0,26&2571&9664&2660&1,31&9662&2579&747&2,36&7044&7098&-0,9924\\ \hline 0,27&2667&9638&2768&1,32&9687&2482&903&2,37&6973&7168&9728\\ \hline 0,28&2764&9611&2875&1,33&9711&2385&4,072&2,38&6901&7237&9535\\ \hline 0,29&2860&9582&2984&1,34&9735&2288&256&2,39&6828&7306&9346\\ \hline &&&&&&&&&&&\\ \hline 0,30&0,2955&0,9553&0.3093&1,35&0,9757&0,2190&4,455&2,40&0,6755&-0,7374&-0,9160\\ \hline 0,31&3051&9523&3203&1,36&9779&2092&673&2,41&6681&7441&8978\\ \hline 0,32&3146&9492&3314&1,37&9799&1994&913&2,42&6606&7508&8799\\ \hline 0,33&3240&9460&3425&1,38&9819&1896&5,177&2,43&6530&7573&8623\\ \hline 0,34&3335&9428&3537&1,39&9837&1798&471&2,44&6454&7638&8450\\ \hline 0,35&0.3429&0,9394&0,3650&1,40&0,9854&0,1700&5,798&2,45&0.6378&-0,7702&-0,8280\\ \hline 0,36&3523&9359&3764&1,41&9871&1601&6.165&2,46&6300&7766&8113\\ \hline 0,37&3616&9323&3879&1,42&9887&1502&6,581&2,47&6222&7828&7949\\ \hline 0,38&3709&9287&3994&1,43&9901&1403&7,055&2,48&6144&7890&7787\\ \hline 0,39&3802&9249&4111&1,44&9915&1304&7.602&2,49&6065&7951&7637\\ \hline X&sin x&cos x&tg x&X&sin x&cos x&tg x&X&sin x&cos x&tg x\\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline X&sin x&cos x&tg x&X&sin x&cos x&tg x&X&sin x&cos x&tg x\\ \hline 0,40&0,3894&0.9211&0,4228&1,45&0,9927&0,1205&8.238&2,50&0,5985&-0,8011&-0,7470\\ \hline 0,41&3986&9171&4346&1,46&9939&1106&8,989&2,51&5904&8071&7316\\ \hline 0,42&4078&9131&4466&1,47&9949&1006&9.887&2,52&5823&8130&7163\\ \hline 0,43&4169&9090&4586&1,48&9959&0907&10,983&2,53&5742&8187&7013\\ \hline 0,44&4259&9048&4708&1,49&9967&0807&12,35&2,54&5660&8244&6865\\ \hline 0,45&0.4350&0.9004&0,4831&1,50&0,9975&0,0707&14.10&2,55&0.5577&-0.8301&-0,6719\\ \hline 0,46&4439&8961&4954&1,51&3982&0608&16,13&2,56&5494&8356&6574\\ \hline 0,47&4529&8916&5080&1,52&9987&0508&19.67&2,57&5410&8410&6432\\ \hline 0,48&4618&8870&5206&1,53&9992&0408&24,50&2,58&5325&8464&6292\\ \hline 0,49&4706&8823&5334&1,54&9995&0308&32,46&2,59&5240&8517&6153\\ \hline &&&&&&&&&&&\\ \hline 0,50&0.4794&0.8776&0.5463&1,55&0,9998&0,0208&48,08&2,60&0.5155&-0,8569&-0,6016\\ \hline 0,51&4882&8727&5594&1,56&0.9999&0,0108&92.62&2,61&5069&8620&5881\\ \hline 0,52&4969&8678&5726&1,57&1,0000&0,0008&1256&2,62&4983&8670&5747\\ \hline 0,53&5055&8628&5859&1,58&1,0000&-0,0092&-108,6&2,63&4896&8720&5615\\ \hline 0,54&5141&8577&5994&1,59&0,9998&-0,0192&-52,07&2,64&4808&8768&5484\\ \hline 0,55&0.5227&0,8525&0,6131&1,60&0,9096&-0,0292&-34,233&2,65&0.4720&-0,8816&-0,5354\\ \hline 0,56&5312&8473&6269&1,61&9992&0392&-25,495&2,66&4632&8863&5226\\ \hline 0,57&5396&8419&6410&1,62&9988&0492&-20,307&2,67&4543&8908&5100\\ \hline 0,58&5480&8365&6552&1,63&9982&0592&-16,871&2,68&4454&8953&4974\\ \hline 0,59&5564&8309&6696&1,64&9976&0691&-14.427&2,69&4364&8998&4850\\ \hline &&&&&&&&&&&\\ \hline 0,60&0,5646&0,8253&0,6841&1,65&0,9969&-0,0791&-12,599&2,70&0,4274&-0,9041&-0,4727\\ \hline 0,61&5729&8196&6989&1,66&9960&0891&-11,181&2,71&4183&9083&4506\\ \hline 0,62&5810&8139&7139&1,67&9951&0990&-10.047&2,72&4092&9124&4485\\ \hline 0,63&5891&8080&7291&1,68&9940&1090&-9.1208&2,73&4001&9165&4365\\ \hline 0,64&5972&8021&7445&1,69&6929&1189&-8,3492&2,74&3909&9204&4247\\ \hline 0,65&0,6052&0,7961&0.7602&1,70&0,9917&-0,1288&-7,6966&2,75&0.3817&-0,9243&-0,4129\\ \hline 0,66&6131&7900&7761&1,71&9903&1388&-7,1373&2,76&3724&9281&4913\\ \hline 0,67&6210&7838&7923&1,72&9889&1486&-6,6524&2,77&3631&9318&3897\\ \hline 0,68&6288&7776&8087&1,73&9874&1585&-6,2281&2,78&3538&9353&3782\\ \hline 0,69&6365&7712&8253&1,74&9857&1684&-5.8535&2,79&3444&9388&3668\\ \hline &&&&&&&&&&&\\ \hline 0,70&0,6442&0,7648&0,8423&1,75&0,9840&-0,1782&-5,5204&2,80&0,335&-0,9422&-0,3555\\ \hline 0,71&6518&7584&8595&1,76&9822&1881&-5,2221&2,81&3256&9455&3443\\ \hline 0,72&6594&7518&8771&1,77&9802&1979&-4.9534&2,82&3161&9487&3332\\ \hline 0,73&6669&7452&8949&1,78&9782&2077&-4.7101&2,83&3066&9519&3221\\ \hline 0,74&6743&7385&9131&1,79&9761&2175&-4,4887&2,84&2970&9549&3111\\ \hline 0,75&0,6816&0.7317&0,9316&1,80&0,9738&-0,2272&-4.2863&2,85&0.2875&-0,9578&-0,3001\\ \hline 0,76&6889&7248&9505&1,81&9715&2369&-4,1005&2,86&2779&9606&2893\\ \hline 0,77&6961&7179&9697&1,82&9691&2466&-3,9294&2,87&2683&9633&2785\\ \hline 0,78&7033&7109&0.9883&1,83&9666&2563&-3,7712&2,88&2586&9660&2677\\ \hline 0,79&7104&7038&1,0092&1,84&9640&2660&-3,6245&2,89&2489&9685&2570\\ \hline &&&&&&&&&&&\\ \hline 0,80 &0,7174 &0,6967 &1,0296 &1,85 &0,9613 &-0,2756 &-3,4881 &2,90 &0,2392 &-0,971 &-0,2464 \\ \hline 0,81 &7243 &6895 &0505 &1,86 &9585 &2852 &-3.3608 &2,91 &2295 &9733 &2358 \\ \hline 0,82 &7311 &6822 &0717 &1,87 &9556 &2948 &-3.2419 &2,92 &2198 &9755 &2253 \\ \hline 0,83 &7379 &6749 &0934 &1,88 &9526 &3043 &-3,1304 &2,93 &2100 &9777 &2148 \\ \hline 0,84 &7446 &6675 &1156 &1,89 &9495 &3138 &-3,0257 &2,94 &2002 &9797 &2044 \\ \hline X&sin x&cos x&tg x&X&sin x&cos x&tg x&X&sin x&cos x&tg x\\ \hline \end{array} \)

Примеры решения проблем

ПРИМЕР 1

Задача

Значение поиска: \(\ \sin 46^{\circ} 30^{\prime} \)

Решение.

В таблице значений синуса и косинуса в первом столбце находим \(\ 46^{\circ} \) и в первой строке \(\ 30^{\prime} \). На пересечении соответствующей строки и столбца находится желаемое значение, равное 0,7254.

Ответ: \(\ \sin 46^{\circ} 30^{\prime}=0,7254 \)

ПРИМЕР 2

Задача

Найти значение: \(\ \cos 76^{\circ} 12^{\prime} \)

Решение.

В таблице значений синуса и косинуса в столбце углов с заголовком cos находим \(\ 76^{\circ} \) и в нижней строке \(\ 12^{\prime} \) . На пересечении соответствующей строки и столбца находится желаемое значение 0.2284.

Ответ: \(\ \cos 76^{\circ} 12^{\prime}=0,2284 \)

Если вам нужно найти значение угла, которого нет в таблице, то выбирается самое близкое к нему значение, а значение коррекции берется из колонки коррекции справа (возможная разница равна 1 ', 2' , 3 ').

ПРИМЕР 3

Задача

Найти значение: \(\ \sin 16^{\circ} 32^{\prime} \)

Решение.

Чтобы вычислить значение: \(\ \sin 16^{\circ} 32^{\prime} \) в таблице, мы найдем значение синуса угла, ближайшего к искомому. Это \(\ \sin 16^{\circ} 30^{\prime}=0,2840 \) . Так как \(\ 16^{\circ} 32^{\prime}=16^{\circ} 3 \dot{0}^{\prime}+2^{\prime} \) , то в столбце поправок выберем \(\ 2^{\prime} \) и видим, что на пересечении с строкой \(\ 16^{\circ} \) равен 0,0006,

\(\ \sin 16^{\circ} 32^{\prime}=\sin \left(16^{\circ} 30^{\prime}+2^{\prime}\right)=0,2840+0,0006=0,2846 \)

Ответ: \(\ \sin 16^{\circ} 32^{\prime}=0,2846 \)

ПРИМЕР 4

Задача

Значение поиска: \(\ \sin 22^{\circ} 10^{\prime} \)

Решение.

Чтобы вычислить значение: \(\ \sin 16^{\circ} 32^{\prime} \) в таблице, мы найдем значение синуса угла, ближайшего к искомому. Это \(\ \sin 22^{\circ} 12^{\prime}=0,3778 \) . Начиная с \(\ 22^{\circ} 10^{\prime}=22^{\circ} 12^{\prime}-2^{\prime} \) , мы выбираем \(\ 2^{\prime} \) в столбце исправлений и видим, что на пересечении с строкой \(\ 22^{\circ} \) равен 0,0005, \(\ \sin 22^{\circ} 10^{\prime}=\sin \left(22^{\circ} 12^{\prime}-2^{\prime}\right)=0,3778+0,0005=0,3773 \)

Ответ: \(\ \sin 22^{\circ} 12^{\prime}=0,3773 \)

Комментарий. Для косинусов коррекция отрицательна.

ПРИМЕР 5

Задача

Найти значение: \(\ \cos 50^{\circ} 33^{\prime} \)

Решение:

Чтобы вычислить значение \(\ \cos 50^{\circ} 33^{\prime} \) в таблице, мы найдем значение косинуса угла, ближайшего к искомому. Это \(\ \cos 50^{\circ} 33^{\prime}=0,6361 \) . Так как \(\ 50^{\circ} 33^{\prime}=50^{\circ} 30^{\prime}+3^{\prime} \) , то в столбце поправок выберите \(\ 3^{\prime} \) и посмотрите, что на пересечении с строкой \(\ 50^{\circ} \) равен 0,0007,

\(\ \cos 50^{\circ} 33^{\prime}=\cos \left(50^{\circ} 30^{\prime}+3^{\prime}\right)=0,6361+(-0,0007)=0,6354 \)

Ответ: \(\ \cos 50^{\circ} 33^{\prime}=0,6354 \)

Эти правила справедливы и для нахождения значений касательных и котангенсов углов.

ПРИМЕР 6

Задача

Найти значение: \(\ \operatorname{tg} 35^{\circ} 6^{\prime} \)

Решение:

В таблице касательных и котангенциальных значений в первом столбце находим \(\ 35^{\circ} \) и в первой строке \(\ 6^{\prime} \) . На пересечении находим искомое значение 0.7028

Ответ \(\ \operatorname{tg} 35^{\circ} 6^{\prime}=0,7028 \)

ПРИМЕР 7

Задача

Найти значение: \(\ \operatorname{ctg} 13^{\circ} 42^{\prime} \)

Решение:

В таблице кокасательных значений малых углов в последнем столбце находим строку \(\ 13^{\circ} 40^{\prime} \) , а в последней строке \(\ 2^{\prime} \) . На пересечении находится желаемое значение 4,102

Ответ: \(\ \operatorname{ctg} 13^{\circ} 42^{\prime}=4,102 \)

Пример 8.

Задача

Найти значение: \(\ \sin 2,3, \cos 3,15 \) \(\ \sin 2,3, \cos 3,15 \)и \(\ \operatorname{tg} 1,67 \)

Решение.

Поскольку в радианах указаны углы, мы используем таблицу значений тригонометрических функций аргумента в радианах. Найти в нем необходимые значения \(\ \sin 2,3=0,7457 \),\(\ \cos 3,12=-0,9998 \) и \(\ \operatorname{tg} 1,67=0,9951 \)

Ответ: \(\ \sin 2,3=0,7457 \), \(\ \cos 3,12=-0,9998 \) и \(\ \operatorname{tg} 1,67=0,9951 \)

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