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Таблица котангенсов

ОПРЕДЕЛЕНИЕ

Котангенс - тригонометрическая функция, равная отношению косинуса к синусу.

При решении математических задач различного характера, а также проблем технического характера часто требуются значения котангенсов разных углов. Таблица содержит рассчитанные значения кокасательных углов от 1 ° до 360 °. Чтобы найти кокасательное значение требуемого угла, просто найдите его в таблице.

Подробная таблица котангенсов

\(\ \begin{array}{|c|c|c|c|c|c|c|c|} \hline Угол&ctg&Угол&ctg& Угол & ctg & Угол & ctg \\ \hline 1^{\circ} &57.29 &46^{\circ} &0.9657 &91^{\circ} &-0.0174 &136^{\circ} &-1.0355\\ \hline 2^{\circ} &28.6363 &47^{\circ} &0.9325 &92^{\circ} &-0.0349 &137^{\circ}&-1.0724 \\ \hline 3^{\circ} &19.0811 &48^{\circ} &0.9004 &93^{\circ} &-0.0524 &138^{\circ} &-1.1106\\ \hline 4^{\circ} &14.3007 &49^{\circ} &0.8693 &94^{\circ} &-0.0699 &139^{\circ} &-1.1504\\ \hline 5^{\circ} &11.4301 &50^{\circ} &0.8390 &95^{\circ} &-0.0874 &140^{\circ}&-1.1918 \\ \hline 6^{\circ} &9.5144 &51^{\circ} &0.8098 &96^{\circ} &-0.1051 &141^{\circ} &-1.2349 \\\hline 7^{\circ} &8.1443 &52^{\circ} &0.7813 &97^{\circ} &-0.1227 &142^{\circ} &-1.2799\\ \hline 8^{\circ} &7.1154 &53^{\circ} &0.7535 &98^{\circ} &-0.1405 &143^{\circ} &-1.327\\ \hline 9^{\circ} &6.3138 &54^{\circ} &0.7265 &99^{\circ} &-0.1583 &144^{\circ} &-1.3764\\ \hline 10^{\circ} &5.6713 &55^{\circ} &0.7002 &100^{\circ} &-0.1763 &145^{\circ}&-1.4281 \\ \hline 11^{\circ} &5.1446 &56^{\circ} &0.6745 &101^{\circ} &-0.1943 &146^{\circ} &-1.4826\\ \hline 12^{\circ} &-4.7046 &57^{\circ} &0.6494 &102^{\circ} &-0.2125 &147^{\circ} &-1.5399\\ \hline 13^{\circ} &4.3315 &58^{\circ} &0.6249 &103^{\circ} &-0.2308 &148^{\circ} &-1.6003\\ \hline 14^{\circ} &4.0108 &59^{\circ} &0.6009 &104^{\circ} &-0.2493 &149^{\circ} &-1.6643\\ \hline 15^{\circ} &3.732 &60^{\circ} &0.5774 &105^{\circ} &-0.2679 &150^{\circ} &-1.7321\\ \hline 16^{\circ} &3.4874 &61^{\circ} &0.5543 &106^{\circ} &-0.2867 &151^{\circ} &-1.804\\ \hline 17^{\circ} &3.2709 &62^{\circ} &0.5317 &107^{\circ} &-0.3057 &152^{\circ} &-1.8807\\ \hline 18^{\circ} &3.0777 &63^{\circ} &0.5095 &108^{\circ} &-0.3249 &153^{\circ} &-1.9626\\ \hline 19^{\circ} &2.9042 &64^{\circ} &0.4877 &109^{\circ} &-0.3443 &154^{\circ} &-2.0503\\ \hline 20^{\circ} &2.7475 &65^{\circ} &0.4663 &110^{\circ} &-0.364 &155^{\circ}&-2.1445 \\ \hline 21^{\circ} &2.605 &66^{\circ} &0.4452 &111^{\circ} &-0.3839 &156^{\circ} &-2.2460\\ \hline 22^{\circ} &2.475 &67^{\circ} &0.4245 &112^{\circ} &-0.404 &157^{\circ} &-2.3559\\ \hline 23^{\circ} &2.3559 &68^{\circ} &0.404 &113^{\circ} &-0.4245 &158^{\circ}&-2.475 \\ \hline 24^{\circ} &2.2460 &69^{\circ} &0.3839 &114^{\circ} &-0.4452 &159^{\circ}&-2.605 \\ \hline 25^{\circ} &2.1445 &70^{\circ} &0.364 &115^{\circ} &-0.4663 &160^{\circ}&-2.7475 \\ \hline 26^{\circ} &2.0503 &71^{\circ} &0.3443 &116^{\circ} &-0.4877 &161^{\circ}&-2.9042 \\ \hline 27^{\circ} &1.9626 &72^{\circ} &0.3249 &117^{\circ} &-0.5095 &162^{\circ}& -3.0777\\ \hline 28^{\circ} &1.8807 &73^{\circ} &0.3057 &118^{\circ} &-0.5317 &163^{\circ} &-3.2709\\ \hline 29^{\circ} &1.804 &74^{\circ} &0.2867 &119^{\circ} &-0.5543 &164^{\circ}& -3.4874\\ \hline 30^{\circ} &1.7321 &75^{\circ} &0.2679 &120^{\circ} &-0.5774 &165^{\circ} &-3.732\\ \hline 31^{\circ} &1.6643 &76^{\circ} &0.2493 &121^{\circ} &-0.6009 &166^{\circ}& -4.0108\\ \hline 32^{\circ} &1.6003 &77^{\circ} &0.2308 &122^{\circ} &-0.6249 &167^{\circ}& -4.3315\\ \hline 33^{\circ} &1.5399 &78^{\circ} &0.2125 &123^{\circ} &-0.6494 &168^{\circ}&-4.7046 \\ \hline 34^{\circ} &1.4826 &79^{\circ} &0.1943 &124^{\circ} &-0.6745 &169^{\circ}& -5.1446\\ \hline 35^{\circ} &1.4281 &80^{\circ} &0.1763 &125^{\circ} &-0.7002 &170^{\circ} &-5.6713\\ \hline 36^{\circ} &1.3764 &81^{\circ} &0.1583 &126^{\circ} &-0.7265 &171^{\circ} &-6.3138\\ \hline 37^{\circ} &1.327 &82^{\circ} &0.1405 &127^{\circ} &-0.7535 &172^{\circ} &-7.1154\\ \hline 38^{\circ} &1.2799 &83^{\circ} &0.1227 &128^{\circ} &-0.7813 &173^{\circ}& -8.1443\\ \hline 39^{\circ} &1.2349 &84^{\circ} &0.1051 &129^{\circ} &-0.8098 &174^{\circ} &-9.5144\\ \hline 40^{\circ} &1.1918 &85^{\circ} &0.0874 &130^{\circ} &-0.8390 &175^{\circ}& -11.4301\\ \hline 41^{\circ} &1.1504 &86^{\circ} &0.0699 &131^{\circ} &-0.8693 &176^{\circ} &-14.3007\\ \hline 42^{\circ} &1.1106 &87^{\circ} &0.0524 &132^{\circ} &-0.9004 &177^{\circ}& -19.0811\\ \hline 43^{\circ} &1.0724 &88^{\circ} &0.0349 &133^{\circ} &-0.9325 &178^{\circ} &-28.6363\\ \hline 44^{\circ} &1.0355 &89^{\circ} &0.0174 &134^{\circ} &-0.9657 &179^{\circ} &-57.29\\ \hline 45^{\circ} &1 &90^{\circ} &0&135^{\circ} &-1 &180^{\circ}& не определен\\ \hline \end{array} \)

\(\ \begin{array}{|c|c|c|c|c|c|c|c|} \hline Угол&ctg&Угол&ctg& Угол & ctg & Угол & ctg \\ \hline 181^{\circ} &57.29 &226^{\circ} &0.9657 &271^{\circ} &-0.0174 &316^{\circ} &-1.0355\\ \hline 182^{\circ} &28.6363 &227^{\circ} &0.9325 &272^{\circ} &-0.0349 &317^{\circ}&-1.0724 \\ \hline 183^{\circ} &19.0811 &228^{\circ} &0.9004 &273^{\circ} &-0.0524 &318^{\circ} &-1.1106\\ \hline 184^{\circ} &14.3007 &229^{\circ} &0.8693 &274^{\circ} &-0.0699 &319^{\circ} &-1.1504\\ \hline 185^{\circ} &11.4301 &230^{\circ} &0.8390 &275^{\circ} &-0.0874 &320^{\circ}&-1.1918 \\ \hline 186^{\circ} &9.5144 &231^{\circ} &0.8098 &276^{\circ} &-0.1051 &321^{\circ} &-1.2349 \\\hline 187^{\circ} &8.1443 &232^{\circ} &0.7813 &277^{\circ} &-0.1227 &322^{\circ} &-1.2799\\ \hline 188^{\circ} &7.1154 &233^{\circ} &0.7535 &278^{\circ} &-0.1405 &323^{\circ} &-1.327\\ \hline 189^{\circ} &6.3138 &234^{\circ} &0.7265 &279^{\circ} &-0.1583 &324^{\circ} &-1.3764\\ \hline 190^{\circ} &5.6713 &235^{\circ} &0.7002 &280^{\circ} &-0.1763 &325^{\circ}&-1.4281 \\ \hline 191^{\circ} &5.1446 &236^{\circ} &0.6745 &281^{\circ} &-0.1943 &326^{\circ} &-1.4826\\ \hline 192^{\circ} &-4.7046 &237^{\circ} &0.6494 &282^{\circ} &-0.2125 &1327^{\circ} &-1.5399\\ \hline 193^{\circ} &4.3315 &238^{\circ} &0.6249 &283^{\circ} &-0.2308 &328^{\circ} &-1.6003\\ \hline 194^{\circ} &4.0108 &239^{\circ} &0.6009 &284^{\circ} &-0.2493 &329^{\circ} &-1.6643\\ \hline 195^{\circ} &3.732 &240^{\circ} &0.5774 &285^{\circ} &-0.2679 &330^{\circ} &-1.7321\\ \hline 196^{\circ} &3.4874 &241^{\circ} &0.5543 &286^{\circ} &-0.2867 &331^{\circ} &-1.804\\ \hline 197^{\circ} &3.2709 &242^{\circ} &0.5317 &287^{\circ} &-0.3057 &332^{\circ} &-1.8807\\ \hline 198^{\circ} &3.0777 &243^{\circ} &0.5095 &288^{\circ} &-0.3249 &333^{\circ} &-1.9626\\ \hline 199^{\circ} &2.9042 &244^{\circ} &0.4877 &289^{\circ} &-0.3443 &334^{\circ} &-2.0503\\ \hline 200^{\circ} &2.7475 &245^{\circ} &0.4663 &290^{\circ} &-0.364 &335^{\circ}&-2.1445 \\ \hline 201^{\circ} &2.605 &246^{\circ} &0.4452 &291^{\circ} &-0.3839 &336^{\circ} &-2.2460\\ \hline 202^{\circ} &2.475 &247^{\circ} &0.4245 &292^{\circ} &-0.404 &337^{\circ} &-2.3559\\ \hline 203^{\circ} &2.3559 &248^{\circ} &0.404 &293^{\circ} &-0.4245 &338^{\circ}&-2.475 \\ \hline 204^{\circ} &2.2460 &249^{\circ} &0.3839 &294^{\circ} &-0.4452 &339^{\circ}&-2.605 \\ \hline 205^{\circ} &2.1445 &250^{\circ} &0.364 &295^{\circ} &-0.4663 &340^{\circ}&-2.7475 \\ \hline 206^{\circ} &2.0503 &251^{\circ} &0.3443 &296^{\circ} &-0.4877 &341^{\circ}&-2.9042 \\ \hline 207^{\circ} &1.9626 &252^{\circ} &0.3249 &297^{\circ} &-0.5095 &342^{\circ}& -3.0777\\ \hline 208^{\circ} &1.8807 &253^{\circ} &0.3057 &298^{\circ} &-0.5317 &343^{\circ} &-3.2709\\ \hline 209^{\circ} &1.804 &254^{\circ} &0.2867 &299^{\circ} &-0.5543 &344^{\circ}& -3.4874\\ \hline 210^{\circ} &1.7321 &255^{\circ} &0.2679 &300^{\circ} &-0.5774 &345^{\circ} &-3.732\\ \hline 211^{\circ} &1.6643 &256^{\circ} &0.2493 &301^{\circ} &-0.6009 &346^{\circ}& -4.0108\\ \hline 212^{\circ} &1.6003 &257^{\circ} &0.2308 &302^{\circ} &-0.6249 &347^{\circ}& -4.3315\\ \hline 213^{\circ} &1.5399 &258^{\circ} &0.2125 &303^{\circ} &-0.6494 &348^{\circ}&-4.7046 \\ \hline 214^{\circ} &1.4826 &259^{\circ} &0.1943 &304^{\circ} &-0.6745 &349^{\circ}& -5.1446\\ \hline 215^{\circ} &1.4281 &260^{\circ} &0.1763 &305^{\circ} &-0.7002 &350^{\circ} &-5.6713\\ \hline 216^{\circ} &1.3764 &261^{\circ} &0.1583 &306^{\circ} &-0.7265 &351^{\circ} &-6.3138\\ \hline 217^{\circ} &1.327 &262^{\circ} &0.1405 &307^{\circ} &-0.7535 &352^{\circ} &-7.1154\\ \hline 218^{\circ} &1.2799 &263^{\circ} &0.1227 &308^{\circ} &-0.7813 &353^{\circ}& -8.1443\\ \hline 219^{\circ} &1.2349 &264^{\circ} &0.1051 &309^{\circ} &-0.8098 &354^{\circ} &-9.5144\\ \hline 220^{\circ} &1.1918 &265^{\circ} &0.0874 &310^{\circ} &-0.8390 &355^{\circ}& -11.4301\\ \hline 221^{\circ} &1.1504 &266^{\circ} &0.0699 &311^{\circ} &-0.8693 &356^{\circ} &-14.3007\\ \hline 222^{\circ} &1.1106 &267^{\circ} &0.0524 &312^{\circ} &-0.9004 &357^{\circ}& -19.0811\\ \hline 223^{\circ} &1.0724 &268^{\circ} &0.0349 &313^{\circ} &-0.9325 &358^{\circ} &-28.6363\\ \hline 224^{\circ} &1.0355 &269^{\circ} &0.0174 &314^{\circ} &-0.9657 &359^{\circ} &-57.29\\ \hline 225^{\circ} &1 &270^{\circ} &0&315^{\circ} &-1 &360^{\circ}& не определен\\ \hline \end{array} \)

Примеры решения проблем

ПРИМЕР 1

  • Задача

    Рассчитать \(\ \operatorname{ctg} 47^{\circ}+\operatorname{ctg} 95^{\circ} \)

  • Решение.

    В таблице находим требуемые углы и их касательные значения: \(\ \operatorname{ctg} 47^{\circ}=0,9325 \) и \(\ \operatorname{ctg} 95^{\circ}=-0,0874 \) .Найдите нужную сумму

    \(\ \operatorname{ctg} 47^{\circ}+\operatorname{ctg} 95^{\circ}=0,9325+(-0,0874)=0,8451 \)

  • Ответ

    \(\ \operatorname{ctg} 47^{\circ}+\operatorname{ctg} 95^{\circ}=0,8451 \)

    ПРИМЕР 2

  • Задача

    Найдите произведение \(\ A \cdot B \) , где \(\ A=\operatorname{ctg} 134^{\circ} \) и \(\ B=\operatorname{ctg} 86^{\circ} \)

  • Решение.

    Используя таблицу, мы находим отдельно значение каждого фактора:

    \(\ A=\operatorname{ctg} 134^{\circ}=-0,9657 \), \(\ B=\operatorname{ctg} 86^{\circ}=0,0699 \)

    Рассчитать продукт

    \(\ A \cdot B=\operatorname{ctg} 134^{0} \cdot \operatorname{ctg} 86^{\circ}=-0,9657 \cdot 0,0699=-0,06750243 \)

  • Ответ

    \(\ A \cdot B=-0,06750243 \)

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