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

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

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