1. Вычислить, отметив угол на окружности: a) sin495°; б) sin(-23π/6); в) sin(-14π/3); г) ctg(13π/4); д) tg(-11π/3)

a) $$sin(495°) = sin(495° - 360°) = sin(135°) = sin(180° - 45°) = sin(45°) = \frac{\sqrt{2}}{2}$$ б) $$sin(-\frac{23\pi}{6}) = -sin(\frac{23\pi}{6}) = -sin(4\pi - \frac{\pi}{6}) = -sin(-\frac{\pi}{6}) = sin(\frac{\pi}{6}) = \frac{1}{2}$$ в) $$sin(-\frac{14\pi}{3}) = -sin(\frac{14\pi}{3}) = -sin(4\pi + \frac{2\pi}{3}) = -sin(\frac{2\pi}{3}) = -sin(\pi - \frac{\pi}{3}) = -sin(\frac{\pi}{3}) = -\frac{\sqrt{3}}{2}$$ г) $$ctg(\frac{13\pi}{4}) = ctg(3\pi + \frac{\pi}{4}) = ctg(\pi + \frac{\pi}{4}) = ctg(\frac{\pi}{4}) = 1$$ д) $$tg(-\frac{11\pi}{3}) = -tg(\frac{11\pi}{3}) = -tg(4\pi - \frac{\pi}{3}) = -tg(-\frac{\pi}{3}) = tg(\frac{\pi}{3}) = \sqrt{3}$$