Страница 160 номер 529, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение
Вычислить: 1) \(\cos 750^\circ\); 2) \(\sin 1140^\circ\); 3) \(\operatorname{tg} 405^\circ\); 4) \(\cos 840^\circ\); 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) \(\cos 750^{\circ} = \cos(720^{\circ} + 30^{\circ}) = \cos 30^{\circ} = \frac{\sqrt{3}}{2};\)
2) \(\sin 1140^{\circ} = \sin(1080^{\circ} + 60^{\circ}) = \sin 60^{\circ} = \frac{\sqrt{3}}{2};\)
3) \(\operatorname{tg} 405^{\circ} = \operatorname{tg}(360^{\circ} + 45^{\circ}) = \operatorname{tg} 45^{\circ} = 1;\)
4) \(\cos 840^{\circ} = \cos(720^{\circ} + 120^{\circ}) = \cos(90^{\circ} + 30^{\circ}) = -\sin 30^{\circ} = -\frac{1}{2};\)
5) \(\sin\frac{47\pi}{6} = \sin\left(8\pi - \frac{\pi}{6}\right) = -\sin\frac{\pi}{6} = -\frac{1}{2};\)
6) \(\operatorname{tg}\frac{25\pi}{4} = \operatorname{tg}\left(6\pi + \frac{\pi}{4}\right) = \operatorname{tg}\frac{\pi}{4} = 1;\)
7) \(\operatorname{ctg}\frac{27\pi}{4} = \operatorname{ctg}\left(7\pi - \frac{\pi}{4}\right) = -\operatorname{ctg}\frac{\pi}{4} = -1;\)
8) \(\cos\frac{21\pi}{4} = \cos\left(5\pi + \frac{\pi}{4}\right) = -\cos\frac{\pi}{4} = -\frac{\sqrt{2}}{2}.\)
