Упр.1078 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1078.
1) cos 150°;
2) sin 135°;
3) ctgl35°;
4) cos 120°;
5) cos225°;
6) sin210°;
7) ctg240°;
8) sin315°.

1. $$\cos 150^\circ=\cos(90^\circ+60^\circ)=-\sin 60^\circ=-\frac{\sqrt{3}}{2}$$
2. $$\sin 135^\circ=\sin(180^\circ-45^\circ)=\sin 45^\circ=\frac{\sqrt{2}}{2}$$
3. $$\ctg 135^\circ=\ctg(90^\circ+45^\circ)=-\tg 45^\circ=-1$$
4. $$\cos 120^\circ=\cos(90^\circ+30^\circ)=-\sin 30^\circ=-\frac{1}{2}$$
5. $$\cos 225^\circ=\cos(180^\circ+45^\circ)=-\cos 45^\circ=-\frac{\sqrt{2}}{2}$$
6. $$\sin 210^\circ=\sin(180^\circ+30^\circ)=-\sin 30^\circ=-\frac{1}{2}$$
7. $$\ctg 240^\circ=\ctg(180^\circ+60^\circ)=\ctg 60^\circ=\frac{\sqrt{3}}{3}$$
8. $$\sin 315^\circ=\sin(360^\circ-45^\circ)=-\sin 45^\circ=-\frac{\sqrt{2}}{2}$$

Ответ

$$\cos 150^\circ=-\frac{\sqrt{3}}{2},\quad \sin 135^\circ=\frac{\sqrt{2}}{2},\quad \ctg 135^\circ=-1,\quad \cos 120^\circ=-\frac{1}{2},$$
$$\cos 225^\circ=-\frac{\sqrt{2}}{2},\quad \sin 210^\circ=-\frac{1}{2},\quad \ctg 240^\circ=\frac{\sqrt{3}}{3},\quad \sin 315^\circ=-\frac{\sqrt{2}}{2}.$$