Записать градусы в радионы 120,135,210,225,240

Лебедев Дмитрий Сергеевич

Учитель математики

Проверено учителем

Для перевода градусов в радианы используется стандартная формула: αrad=αdegπ180alpha sub r a d end-sub equals alpha sub d e g end-sub center dot the fraction with numerator pi and denominator 180 end-fraction Ниже представлен пошаговый расчет для каждого значения с сокращением дробей. 1. 120 градусов 120=120π180=120π180120 raised to the composed with power equals 120 center dot the fraction with numerator pi and denominator 180 end-fraction equals the fraction with numerator 120 pi and denominator 180 end-fraction Сокращаем на 60: Результат: 2π3the fraction with numerator 2 pi and denominator 3 end-fraction 2. 135 градусов 135=135π180=135π180135 raised to the composed with power equals 135 center dot the fraction with numerator pi and denominator 180 end-fraction equals the fraction with numerator 135 pi and denominator 180 end-fraction Сокращаем на 45: Результат: 3π4the fraction with numerator 3 pi and denominator 4 end-fraction 3. 210 градусов 210=210π180=210π180210 raised to the composed with power equals 210 center dot the fraction with numerator pi and denominator 180 end-fraction equals the fraction with numerator 210 pi and denominator 180 end-fraction Сокращаем на 30: Результат: 7π6the fraction with numerator 7 pi and denominator 6 end-fraction 4. 225 градусов 225=225π180=225π180225 raised to the composed with power equals 225 center dot the fraction with numerator pi and denominator 180 end-fraction equals the fraction with numerator 225 pi and denominator 180 end-fraction Сокращаем на 45: Результат: 5π4the fraction with numerator 5 pi and denominator 4 end-fraction 5. 240 градусов 240=240π180=240π180240 raised to the composed with power equals 240 center dot the fraction with numerator pi and denominator 180 end-fraction equals the fraction with numerator 240 pi and denominator 180 end-fraction Сокращаем на 60: Результат: 4π3the fraction with numerator 4 pi and denominator 3 end-fraction Сводная таблица

Градусы Радианы (дробь)Радианы (десятичные, π3.14pi is approximately equal to 3.14)
120° 2π3the fraction with numerator 2 pi and denominator 3 end-fraction 2.094is approximately equal to 2.094
135° 3π4the fraction with numerator 3 pi and denominator 4 end-fraction 2.356is approximately equal to 2.356
210° 7π6the fraction with numerator 7 pi and denominator 6 end-fraction 3.665is approximately equal to 3.665
225° 5π4the fraction with numerator 5 pi and denominator 4 end-fraction 3.927is approximately equal to 3.927
240° 4π3the fraction with numerator 4 pi and denominator 3 end-fraction 4.188is approximately equal to 4.188

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