Упр.548 ГДЗ Алимов 10-11 класс (Алгебра)

548 1) sin 47пи/6;
2) tg 25пи/4;
3) ctg 27пи/4;
4) cos 21пи/4.

1. $$\sin \frac{47\pi}{6}=\sin\left(8\pi-\frac{\pi}{6}\right)=\sin\left(-\frac{\pi}{6}\right)=-\sin\frac{\pi}{6}=-\frac12.$$

2. $$\tg \frac{25\pi}{4}=\tg\left(6\pi+\frac{\pi}{4}\right)=\tg\frac{\pi}{4}=1.$$

3. $$\ctg \frac{27\pi}{4}=\ctg\left(7\pi-\frac{\pi}{4}\right)=\ctg\left(-\frac{\pi}{4}\right)=-\ctg\frac{\pi}{4}=-1.$$

4. $$\cos \frac{21\pi}{4}=\cos\left(5\pi+\frac{\pi}{4}\right)=-\cos\frac{\pi}{4}=-\frac{\sqrt2}{2}.$$

Ответ

$$-\frac12,\ 1,\ -1,\ -\frac{\sqrt2}{2}$$