531 Вычислить: 23 π 1) cos 4 15 π sin 4 ctg π 11π 2 ); 2) sin 25-cos(-17) - tg 10%; 3 3 3) sin (-7π) – 2 cos 31π 3 7π; tg; 4 4) cos (-9π) + 2 sin 49 π 6 ) 21π ctg(- 4

Решение заданий 531: 1) $$cos \frac{23\pi}{4} - sin \frac{15\pi}{4} - ctg(-\frac{11\pi}{2})$$ * $$cos \frac{23\pi}{4} = cos (5\pi + \frac{3\pi}{4}) = -cos \frac{3\pi}{4} = \frac{\sqrt{2}}{2}$$ * $$sin \frac{15\pi}{4} = sin (3\pi + \frac{3\pi}{4}) = -sin \frac{3\pi}{4} = -\frac{\sqrt{2}}{2}$$ * $$ctg(-\frac{11\pi}{2}) = -ctg(\frac{11\pi}{2}) = -ctg(5\pi + \frac{\pi}{2}) = -ctg(\frac{\pi}{2}) = 0$$ $$\frac{\sqrt{2}}{2} - (-\frac{\sqrt{2}}{2}) - 0 = \sqrt{2}$$ 2) $$sin \frac{25\pi}{3} - cos(-\frac{17\pi}{2}) - tg \frac{10\pi}{3}$$ * $$sin \frac{25\pi}{3} = sin(8\pi + \frac{\pi}{3}) = sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$$ * $$cos(-\frac{17\pi}{2}) = cos(\frac{17\pi}{2}) = cos(8\pi + \frac{\pi}{2}) = cos \frac{\pi}{2} = 0$$ * $$tg \frac{10\pi}{3} = tg(3\pi + \frac{\pi}{3}) = tg \frac{\pi}{3} = \sqrt{3}$$ $$\frac{\sqrt{3}}{2} - 0 - \sqrt{3} = -\frac{\sqrt{3}}{2}$$ 3) $$sin (-7\pi) - 2cos \frac{31\pi}{3} - tg \frac{7\pi}{4}$$ * $$sin(-7\pi) = -sin(7\pi) = -sin(\pi) = 0$$ * $$cos \frac{31\pi}{3} = cos (10\pi + \frac{\pi}{3}) = cos \frac{\pi}{3} = \frac{1}{2}$$ * $$tg \frac{7\pi}{4} = tg (2\pi - \frac{\pi}{4}) = -tg \frac{\pi}{4} = -1$$ $$0 - 2 \cdot \frac{1}{2} - (-1) = 0 - 1 + 1 = 0$$ 4) $$cos (-9\pi) + 2sin(-\frac{49\pi}{6}) - ctg(-\frac{21\pi}{4})$$ * $$cos (-9\pi) = cos (9\pi) = cos (\pi) = -1$$ * $$sin(-\frac{49\pi}{6}) = -sin(\frac{49\pi}{6}) = -sin(8\pi + \frac{\pi}{6}) = -sin \frac{\pi}{6} = -\frac{1}{2}$$ * $$ctg(-\frac{21\pi}{4}) = -ctg(\frac{21\pi}{4}) = -ctg(5\pi + \frac{\pi}{4}) = -ctg \frac{\pi}{4} = -1$$ $$-1 + 2 \cdot (-\frac{1}{2}) - (-1) = -1 - 1 + 1 = -1$$ Ответ: 1) $$\sqrt{2}$$ 2) $$\frac{-\sqrt{3}}{2}$$ 3) $$0$$ 4) $$-1$$