2) $\frac{7\pi}{6} =$ $\frac{5\pi}{6} =$ $\frac{\pi}{6} =$ $\frac{14\pi}{6} =$ g) $\frac{8\pi}{3} =$ $\frac{\pi}{3} =$ $\frac{3\pi}{3} =$ $\frac{17\pi}{3} =$ e) $-\frac{\pi}{18} =$ $-\frac{21\pi}{18} =$ $-\frac{17\pi}{12} =$ $-\frac{13\pi}{9} =$ Выразите в градусах величину угла:

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Ответ:

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Accepted Answer

Для перевода радианной меры угла в градусную, нужно воспользоваться формулой:

$$ \alpha^{\circ} = \alpha \cdot \frac{180^{\circ}}{\pi} $$

2) $\frac{7\pi}{6} =$

$\frac{7\pi}{6} = \frac{7 \cdot 180^{\circ}}{6} = 7 \cdot 30^{\circ} = 210^{\circ} $

$\frac{5\pi}{6} = \frac{5 \cdot 180^{\circ}}{6} = 5 \cdot 30^{\circ} = 150^{\circ} $

$\frac{\pi}{6} = \frac{180^{\circ}}{6} = 30^{\circ} $

$\frac{14\pi}{6} = \frac{14 \cdot 180^{\circ}}{6} = 14 \cdot 30^{\circ} = 420^{\circ} $

g) $\frac{8\pi}{3} =$

$\frac{8\pi}{3} = \frac{8 \cdot 180^{\circ}}{3} = 8 \cdot 60^{\circ} = 480^{\circ} $

$\frac{\pi}{3} = \frac{180^{\circ}}{3} = 60^{\circ} $

$\frac{3\pi}{3} = \frac{3 \cdot 180^{\circ}}{3} = 180^{\circ} $

$\frac{17\pi}{3} = \frac{17 \cdot 180^{\circ}}{3} = 17 \cdot 60^{\circ} = 1020^{\circ} $

e) $-\frac{\pi}{18} =$

$-\frac{\pi}{18} = -\frac{180^{\circ}}{18} = -10^{\circ} $

$-\frac{21\pi}{18} = -\frac{21 \cdot 180^{\circ}}{18} = -21 \cdot 10^{\circ} = -210^{\circ} $

$-\frac{17\pi}{12} = -\frac{17 \cdot 180^{\circ}}{12} = -17 \cdot 15^{\circ} = -255^{\circ} $

$-\frac{13\pi}{9} = -\frac{13 \cdot 180^{\circ}}{9} = -13 \cdot 20^{\circ} = -260^{\circ} $

Ответ:

2) $\frac{7\pi}{6} = 210^{\circ} $, $\frac{5\pi}{6} = 150^{\circ} $, $\frac{\pi}{6} = 30^{\circ} $, $\frac{14\pi}{6} = 420^{\circ} $

g) $\frac{8\pi}{3} = 480^{\circ} $, $\frac{\pi}{3} = 60^{\circ} $, $\frac{3\pi}{3} = 180^{\circ} $, $\frac{17\pi}{3} = 1020^{\circ} $

e) $-\frac{\pi}{18} = -10^{\circ} $, $-\frac{21\pi}{18} = -210^{\circ} $, $-\frac{17\pi}{12} = -255^{\circ} $, $-\frac{13\pi}{9} = -260^{\circ} $