Упр.481 ГДЗ Алимов 10-11 класс (Алгебра)

1) cos 135°; 2) cos 120°; 3) cos 150°; 4) cos 240°.

1. $$\cos 135^\circ=\cos(90^\circ+45^\circ)=\cos 90^\circ\cos 45^\circ-\sin 90^\circ\sin 45^\circ$$
   $$=0\cdot \frac{\sqrt2}{2}-1\cdot \frac{\sqrt2}{2}=-\frac{\sqrt2}{2}.$$
2. $$\cos 120^\circ=\cos(90^\circ+30^\circ)=\cos 90^\circ\cos 30^\circ-\sin 90^\circ\sin 30^\circ$$
   $$=0\cdot \frac{\sqrt3}{2}-1\cdot \frac12=-\frac12.$$
3. $$\cos 150^\circ=\cos(90^\circ+60^\circ)=\cos 90^\circ\cos 60^\circ-\sin 90^\circ\sin 60^\circ$$
   $$=0\cdot \frac12-1\cdot \frac{\sqrt3}{2}=-\frac{\sqrt3}{2}.$$
4. $$\cos 240^\circ=\cos(180^\circ+60^\circ)=\cos 180^\circ\cos 60^\circ-\sin 180^\circ\sin 60^\circ$$
   $$=-1\cdot \frac12-0\cdot \frac{\sqrt3}{2}=-\frac12.$$

Ответ

$$\cos 135^\circ=-\frac{\sqrt2}{2},\quad \cos 120^\circ=-\frac12,\quad \cos 150^\circ=-\frac{\sqrt3}{2},\quad \cos 240^\circ=-\frac12.$$