Упр.1079 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

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

1. $$\tg \frac{5\pi}{4}=\tg\left(\pi+\frac{\pi}{4}\right)=\tg \frac{\pi}{4}=1.$$
2. $$\sin \frac{7\pi}{6}=\sin\left(\pi+\frac{\pi}{6}\right)=-\sin \frac{\pi}{6}=-\frac12.$$
3. $$\cos \frac{5\pi}{3}=\cos\left(2\pi-\frac{\pi}{3}\right)=\cos \frac{\pi}{3}=\frac12.$$
4. $$\ctg \frac{5\pi}{3}=\ctg\left(2\pi-\frac{\pi}{3}\right)=-\ctg \frac{\pi}{3}=-\frac{\sqrt3}{3}.$$
5. $$\sin\left(-\frac{13\pi}{6}\right)=\sin\left(-2\pi-\frac{\pi}{6}\right)=-\sin \frac{\pi}{6}=-\frac12.$$
6. $$\cos\left(-\frac{7\pi}{3}\right)=\cos\left(-2\pi-\frac{\pi}{3}\right)=\cos \frac{\pi}{3}=\frac12.$$
7. $$\tg\left(-\frac{2\pi}{3}\right)=\tg\left(-\pi+\frac{\pi}{3}\right)=\tg \frac{\pi}{3}=\sqrt3.$$
8. $$\ctg\left(-\frac{7\pi}{4}\right)=\ctg\left(-2\pi+\frac{\pi}{4}\right)=\ctg \frac{\pi}{4}=1.$$

Ответ

$$1;\ -\frac12;\ \frac12;\ -\frac{\sqrt3}{3};\ -\frac12;\ \frac12;\ \sqrt3;\ 1.$$