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

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