1. Вычислить, отметив угол на окружности: a) sin840°; 6) sin(-17 Π/4); в) sin(-16 п/3) ctg 7π/3; д) tg(-19/7/6)

1. Вычислить, отметив угол на окружности:

a) $$sin840^\circ$$

$$sin840^\circ = sin(2 \cdot 360^\circ + 120^\circ) = sin120^\circ = sin(180^\circ - 60^\circ) = sin60^\circ = \frac{\sqrt{3}}{2}$$

Ответ: $$\frac{\sqrt{3}}{2}$$

б) $$sin(-\frac{17\pi}{4})$$

$$sin(-\frac{17\pi}{4}) = -sin(\frac{17\pi}{4}) = -sin(4\pi + \frac{\pi}{4}) = -sin(\frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$$

Ответ: $$- \frac{\sqrt{2}}{2}$$

в) $$sin(-\frac{16\pi}{3})$$

$$sin(-\frac{16\pi}{3}) = -sin(\frac{16\pi}{3}) = -sin(5\pi + \frac{\pi}{3}) = -sin(4\pi + \pi + \frac{\pi}{3}) = -sin(\pi + \frac{\pi}{3}) = -(-sin(\frac{\pi}{3})) = sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$$

Ответ: $$\frac{\sqrt{3}}{2}$$

г) $$ctg(\frac{7\pi}{3})$$

$$ctg(\frac{7\pi}{3}) = ctg(2\pi + \frac{\pi}{3}) = ctg(\frac{\pi}{3}) = \frac{\sqrt{3}}{3}$$

Ответ: $$\frac{\sqrt{3}}{3}$$

д) $$tg(-\frac{19\pi}{6})$$

$$tg(-\frac{19\pi}{6}) = -tg(\frac{19\pi}{6}) = -tg(3\pi + \frac{\pi}{6}) = -tg(2\pi + \pi + \frac{\pi}{6}) = -tg(\pi + \frac{\pi}{6}) = -tg(\frac{\pi}{6}) = -\frac{\sqrt{3}}{3}$$

Ответ: $$\frac{-\sqrt{3}}{3}$$