Упр.1082 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1) sin 1140°;
2) cos840°;
3) tg 25пи/4;
4) cos 21пи/4.

1) $$\sin 1140^\circ=\sin(1080^\circ+60^\circ)=\sin 60^\circ=\frac{\sqrt{3}}{2}.$$

2) $$\cos 840^\circ=\cos(720^\circ+120^\circ)=\cos 120^\circ=\cos(180^\circ-60^\circ)=-\cos 60^\circ=-\frac{1}{2}.$$

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

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

Ответ

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