Перевод радианной меры угла в градусную

Задание 2. Выразить в градусной мере величины углов. Для перевода из радианной меры в градусную используется формула: \[ \alpha^\circ = \frac{\alpha_{рад} \cdot 180^\circ}{\pi} \] Это означает, что вместо \( \pi \) нужно подставить \( 180^\circ \). Решение: а) \[ \frac{7\pi}{6} = \frac{7 \cdot 180^\circ}{6} = 7 \cdot 30^\circ = 210^\circ \] \[ -\frac{\pi}{5} = -\frac{180^\circ}{5} = -36^\circ \] \[ 0,3\pi = 0,3 \cdot 180^\circ = 54^\circ \] б) \[ \frac{5\pi}{18} = \frac{5 \cdot 180^\circ}{18} = 5 \cdot 10^\circ = 50^\circ \] \[ -\frac{7\pi}{9} = -\frac{7 \cdot 180^\circ}{9} = -7 \cdot 20^\circ = -140^\circ \] \[ 0,2\pi = 0,2 \cdot 180^\circ = 36^\circ \] в) \[ \frac{5\pi}{9} = \frac{5 \cdot 180^\circ}{9} = 5 \cdot 20^\circ = 100^\circ \] \[ -\frac{11\pi}{18} = -\frac{11 \cdot 180^\circ}{18} = -11 \cdot 10^\circ = -110^\circ \] \[ 1,4\pi = 1,4 \cdot 180^\circ = 252^\circ \] г) \[ \frac{5\pi}{36} = \frac{5 \cdot 180^\circ}{36} = 5 \cdot 5^\circ = 25^\circ \] \[ -\frac{4\pi}{5} = -\frac{4 \cdot 180^\circ}{5} = -4 \cdot 36^\circ = -144^\circ \] \[ 1,5\pi = 1,5 \cdot 180^\circ = 270^\circ \] д) \[ \frac{7\pi}{9} = \frac{7 \cdot 180^\circ}{9} = 7 \cdot 20^\circ = 140^\circ \] \[ -\frac{2\pi}{3} = -\frac{2 \cdot 180^\circ}{3} = -2 \cdot 60^\circ = -120^\circ \] \[ 0,8\pi = 0,8 \cdot 180^\circ = 144^\circ \] е) \[ \frac{7\pi}{36} = \frac{7 \cdot 180^\circ}{36} = 7 \cdot 5^\circ = 35^\circ \] \[ -\frac{5\pi}{18} = -\frac{5 \cdot 180^\circ}{18} = -5 \cdot 10^\circ = -50^\circ \] \[ 1,7\pi = 1,7 \cdot 180^\circ = 306^\circ \] ж) \[ \frac{2\pi}{3} = \frac{2 \cdot 180^\circ}{3} = 2 \cdot 60^\circ = 120^\circ \] \[ -\frac{4\pi}{5} = -\frac{4 \cdot 180^\circ}{5} = -4 \cdot 36^\circ = -144^\circ \] \[ 0,25\pi = 0,25 \cdot 180^\circ = 45^\circ \] з) \[ \frac{8\pi}{9} = \frac{8 \cdot 180^\circ}{9} = 8 \cdot 20^\circ = 160^\circ \] \[ -\frac{\pi}{6} = -\frac{180^\circ}{6} = -30^\circ \] \[ 0,125\pi = 0,125 \cdot 180^\circ = 22,5^\circ \] и) \[ \frac{\pi}{18} = \frac{180^\circ}{18} = 10^\circ \] \[ -\frac{6\pi}{5} = -\frac{6 \cdot 180^\circ}{5} = -6 \cdot 36^\circ = -216^\circ \] \[ 0,6\pi = 0,6 \cdot 180^\circ = 108^\circ \] к) \[ \frac{5\pi}{3} = \frac{5 \cdot 180^\circ}{3} = 5 \cdot 60^\circ = 300^\circ \] \[ -\frac{\pi}{3} = -\frac{180^\circ}{3} = -60^\circ \] \[ 0,4\pi = 0,4 \cdot 180^\circ = 72^\circ \] л) \[ \frac{19\pi}{36} = \frac{19 \cdot 180^\circ}{36} = 19 \cdot 5^\circ = 95^\circ \] \[ -\frac{7\pi}{6} = -\frac{7 \cdot 180^\circ}{6} = -7 \cdot 30^\circ = -210^\circ \] \[ 1,1\pi = 1,1 \cdot 180^\circ = 198^\circ \] м) \[ \frac{\pi}{3} = \frac{180^\circ}{3} = 60^\circ \] \[ -\frac{13\pi}{18} = -\frac{13 \cdot 180^\circ}{18} = -13 \cdot 10^\circ = -130^\circ \] \[ 1,25\pi = 1,25 \cdot 180^\circ = 225^\circ \]