5 Вычислите: a) \(sin 225^\circ + cos 330^\circ + ctg 510^\circ\) б) \(sin \frac{17\pi}{6} + cos \frac{14\pi}{3} - tg \frac{13\pi}{4}\)

1. а) \(sin 225^\circ + cos 330^\circ + ctg 510^\circ\)
   \(sin 225^\circ = sin (180^\circ + 45^\circ) = -sin 45^\circ = -\frac{\sqrt{2}}{2}\) \(cos 330^\circ = cos (360^\circ - 30^\circ) = cos 30^\circ = \frac{\sqrt{3}}{2}\) \(ctg 510^\circ = ctg (360^\circ + 150^\circ) = ctg 150^\circ = ctg (180^\circ - 30^\circ) = -ctg 30^\circ = -\sqrt{3}\) \(sin 225^\circ + cos 330^\circ + ctg 510^\circ = -\frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{2} - \sqrt{3} = -\frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2}\)
2. б) \(sin \frac{17\pi}{6} + cos \frac{14\pi}{3} - tg \frac{13\pi}{4}\)
   \(sin \frac{17\pi}{6} = sin (2\pi + \frac{5\pi}{6}) = sin \frac{5\pi}{6} = sin (\pi - \frac{\pi}{6}) = sin \frac{\pi}{6} = \frac{1}{2}\) \(cos \frac{14\pi}{3} = cos (4\pi + \frac{2\pi}{3}) = cos \frac{2\pi}{3} = cos (\pi - \frac{\pi}{3}) = -cos \frac{\pi}{3} = -\frac{1}{2}\) \(tg \frac{13\pi}{4} = tg (3\pi + \frac{\pi}{4}) = tg \frac{\pi}{4} = 1\) \(sin \frac{17\pi}{6} + cos \frac{14\pi}{3} - tg \frac{13\pi}{4} = \frac{1}{2} - \frac{1}{2} - 1 = -1\)

Ответ: а) \(-\frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2}\); б) -1