Упр.525 ГДЗ Алимов 10-11 класс (Алгебра)

1. 525. Вычислить с помощью формулы приведения: 1) $$\cos 150^\circ$$; 2) $$\sin 135^\circ$$; 3) $$\operatorname{ctg} 135^\circ$$; 4) $$\cos 120^\circ$$; 5) $$\cos 225^\circ$$; 6) $$\sin 210^\circ$$; 7) $$\operatorname{ctg} 240^\circ$$; 8) $$\sin 315^\circ$$.

1. $$\cos 150^\circ=\cos(180^\circ-30^\circ)=-\cos 30^\circ=-\frac{\sqrt{3}}{2}$$

2. $$\sin 135^\circ=\sin(90^\circ+45^\circ)=\cos 45^\circ=\frac{\sqrt{2}}{2}$$

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. $$\ctg 240^\circ=\ctg(180^\circ+60^\circ)=\ctg 60^\circ=\frac{1}{\sqrt{3}}$$

8. $$\sin 315^\circ=\sin(270^\circ+45^\circ)=-\cos 45^\circ=-\frac{\sqrt{2}}{2}$$

Ответ: $$-\frac{\sqrt{3}}{2},\ \frac{\sqrt{2}}{2},\ -1,\ -\frac{1}{2},\ -\frac{\sqrt{2}}{2},\ -\frac{1}{2},\ \frac{1}{\sqrt{3}},\ -\frac{\sqrt{2}}{2}$$