529 Вычислить: 1) cos 750°; 5) sin 47π; 6 2) sin 1140°; 25π. 6) tg 4 3) tg 405°; 27π; 7) ctg 4 4) cos 840°; 21π 8) cos 4

Решение заданий 529: 1) $$cos 750° = cos (720° + 30°) = cos (2 \cdot 360° + 30°) = cos 30° = \frac{\sqrt{3}}{2}$$ 2) $$sin 1140° = sin (3 \cdot 360° + 60°) = sin 60° = \frac{\sqrt{3}}{2}$$ 3) $$tg 405° = tg (360° + 45°) = tg 45° = 1$$ 4) $$cos 840° = cos (2 \cdot 360° + 120°) = cos 120° = -\frac{1}{2}$$ 5) $$sin \frac{47\pi}{6} = sin (8\pi - \frac{\pi}{6}) = sin(-\frac{\pi}{6}) = -sin(\frac{\pi}{6}) = -\frac{1}{2}$$ 6) $$tg \frac{25\pi}{4} = tg (6\pi + \frac{\pi}{4}) = tg(\frac{\pi}{4}) = 1$$ 7) $$ctg \frac{27\pi}{4} = ctg (6\pi + \frac{3\pi}{4}) = ctg(\frac{3\pi}{4}) = -1$$ 8) $$cos \frac{21\pi}{4} = cos (5\pi + \frac{\pi}{4}) = cos(\pi + \frac{\pi}{4}) = -cos(\frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$$ Ответ: 1) $$\frac{\sqrt{3}}{2}$$ 2) $$\frac{\sqrt{3}}{2}$$ 3) $$1$$ 4) $$\frac{-1}{2}$$ 5) $$\frac{-1}{2}$$ 6) $$1$$ 7) $$-1$$ 8) $$\frac{-\sqrt{2}}{2}$$