Упр.526 ГДЗ Алимов 10-11 класс (Алгебра)

2)sin 7пи/6;
3) cos 5пи/3;
4) ctg 5 пи/3;
5) sin (-13пи/6);
6) cos (-7 пи/3);
7) tg (-2 пи/3);
8) ctg (-7пи/4).

1. $$\tg \frac{5\pi}{4}=\tg\left(\pi+\frac{\pi}{4}\right)=\tg \frac{\pi}{4}=1.$$
2. $$\sin \frac{7\pi}{6}=\sin\left(\pi+\frac{\pi}{6}\right)=-\sin \frac{\pi}{6}=-\frac{1}{2}.$$
3. $$\cos \frac{5\pi}{3}=\cos\left(2\pi-\frac{\pi}{3}\right)=\cos \frac{\pi}{3}=\frac{1}{2}.$$
4. $$\ctg \frac{5\pi}{3}=\ctg\left(2\pi-\frac{\pi}{3}\right)=-\ctg \frac{\pi}{3}=-\frac{\sqrt{3}}{3}.$$
5. $$\sin\left(-\frac{13\pi}{6}\right)=\sin\left(-2\pi-\frac{\pi}{6}\right)=-\sin \frac{\pi}{6}=-\frac{1}{2}.$$
6. $$\cos\left(-\frac{7\pi}{3}\right)=\cos\left(-2\pi-\frac{\pi}{3}\right)=\cos \frac{\pi}{3}=\frac{1}{2}.$$
7. $$\tg\left(-\frac{2\pi}{3}\right)=\tg\left(-\pi+\frac{\pi}{3}\right)=\tg \frac{\pi}{3}=\sqrt{3}.$$
8. $$\ctg\left(-\frac{7\pi}{4}\right)=\ctg\left(-2\pi+\frac{\pi}{4}\right)=\ctg \frac{\pi}{4}=1.$$

Ответ

$$1;\ -\frac{1}{2};\ \frac{1}{2};\ -\frac{\sqrt{3}}{3};\ -\frac{1}{2};\ \frac{1}{2};\ \sqrt{3};\ 1.$$