1. Вычислить, отметив угол на окружности: a) sin495°; 6) sin -23π ; 6 в) sin(-14π 3 13π д) 11π. г) ctg ; tg -

Ответ:

1. a) sin495° \[\sin(495^\circ) = \sin(495^\circ - 360^\circ) = \sin(135^\circ) = \sin(180^\circ - 45^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2}\]
2. б) sin(-23π/6) \[\sin\left(-\frac{23\pi}{6}\right) = -\sin\left(\frac{23\pi}{6}\right) = -\sin\left(4\pi - \frac{\pi}{6}\right) = -\sin\left(-\frac{\pi}{6}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}\]
3. в) sin(-14π/3) \[\sin\left(-\frac{14\pi}{3}\right) = -\sin\left(\frac{14\pi}{3}\right) = -\sin\left(4\pi + \frac{2\pi}{3}\right) = -\sin\left(\frac{2\pi}{3}\right) = -\sin\left(\pi - \frac{\pi}{3}\right) = -\sin\left(\frac{\pi}{3}\right) = -\frac{\sqrt{3}}{2}\]
4. г) ctg(13π/4) \[\operatorname{ctg}\left(\frac{13\pi}{4}\right) = \operatorname{ctg}\left(3\pi + \frac{\pi}{4}\right) = \operatorname{ctg}\left(\pi + \frac{\pi}{4}\right) = \operatorname{ctg}\left(\frac{\pi}{4}\right) = 1\]
5. д) tg(11π/3) \[\operatorname{tg}\left(\frac{11\pi}{3}\right) = \operatorname{tg}\left(4\pi - \frac{\pi}{3}\right) = \operatorname{tg}\left(-\frac{\pi}{3}\right) = -\operatorname{tg}\left(\frac{\pi}{3}\right) = -\sqrt{3}\]

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