Упр.529 ГДЗ Алимов 10-11 класс (Алгебра)

1. Вычислить: 1) $$\cos 75^\circ$$; 2) $$\sin 114^\circ$$; 3) $$\operatorname{tg} 405^\circ$$; 4) $$\cos 84^\circ$$; 5) $$\sin \frac{47\pi}{6}$$; 6) $$\operatorname{tg} \frac{25\pi}{4}$$; 7) $$\operatorname{ctg} \frac{27\pi}{4}$$; 8) $$\cos \frac{21\pi}{4}$$.

1) $$\cos 750^\circ=\cos(720^\circ+30^\circ)=\cos 30^\circ=\frac{\sqrt3}{2}$$

2) $$\sin 1140^\circ=\sin(1080^\circ+60^\circ)=\sin 60^\circ=\frac{\sqrt3}{2}$$

3) $$\tg 405^\circ=\tg(360^\circ+45^\circ)=\tg 45^\circ=1$$

4) $$\cos 840^\circ=\cos(720^\circ+120^\circ)=\cos 120^\circ=\cos(180^\circ-60^\circ)=-\cos 60^\circ=-\frac12$$

5) $$\sin \frac{47\pi}{6}=\sin\left(8\pi-\frac{\pi}{6}\right)=\sin\left(-\frac{\pi}{6}\right)=-\sin\frac{\pi}{6}=-\frac12$$

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

7) $$\ctg \frac{27\pi}{4}=\ctg\left(7\pi-\frac{\pi}{4}\right)=\ctg\left(-\frac{\pi}{4}\right)=-\ctg\frac{\pi}{4}=-1$$

8) $$\cos \frac{21\pi}{4}=\cos\left(4\pi+\pi+\frac{\pi}{4}\right)=\cos\left(\pi+\frac{\pi}{4}\right)=-\cos\frac{\pi}{4}=-\frac{\sqrt2}{2}$$

Ответ: $$\frac{\sqrt3}{2},\ \frac{\sqrt3}{2},\ 1,\ -\frac12,\ -\frac12,\ 1,\ -1,\ -\frac{\sqrt2}{2}$$