Страница 159 номер 524, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение
Найти значение острого угла \(\alpha\), если: 1) \(\cos 75^\circ = \cos (90^\circ - \alpha)\); 2) \(\sin 150^\circ = \sin (90^\circ + \alpha)\); 3) \(\sin 150^\circ = \sin (180^\circ - \alpha)\); 4) \(\cos 310^\circ = \cos (270^\circ + \alpha)\); 5) \(\sin\frac{5}{4}\pi = \sin (\pi + \alpha)\); 6) \(\operatorname{tg}\frac{\pi}{5} = \operatorname{tg}\left(\frac{\pi}{2} - \alpha\right)\); 7) \(\cos\frac{7\pi}{4} = \cos\left(\frac{3}{2}\pi + \alpha\right)\); 8) \(\operatorname{ctg}\frac{11}{6}\pi = \operatorname{ctg} (2\pi - \alpha)\).
1) \(\cos 75^{\circ} = \cos(90^{\circ} - \alpha)\)
\(\alpha = 15^{\circ};\)
2) \(\sin 150^{\circ} = \sin(90^{\circ} + \alpha)\)
\(\alpha = 60^{\circ};\)
3) \(\sin 150^{\circ} = \sin(180^{\circ} - \alpha)\)
\(\alpha = 30^{\circ};\)
4) \(\cos 310^{\circ} = \cos(270^{\circ} + \alpha)\)
\(\alpha = 40^{\circ};\)
5) \(\sin\frac{5}{4}\pi = \sin(\pi + \alpha)\)
\(\alpha = \dfrac{\pi}{4};\)
6) \(\operatorname{tg}\frac{\pi}{5} = \operatorname{tg}\left(\frac{\pi}{2} - \alpha\right)\)
\(\alpha = \dfrac{\pi}{2} - \dfrac{\pi}{5} = \dfrac{3\pi}{10};\)
7) \(\cos\frac{7\pi}{4} = \cos\left(\frac{3\pi}{2} + \alpha\right)\)
\(\alpha = \dfrac{7\pi}{4} - \dfrac{3\pi}{2} = \dfrac{\pi}{4};\)
8) \(\operatorname{ctg}\frac{11}{6}\pi = \operatorname{ctg}(2\pi - \alpha)\)
\(\alpha = 2\pi - \dfrac{11\pi}{6} = \dfrac{\pi}{6}.\)
