1. Вычислить, отметив угол на окружности: a) cos 510°; 6) sin \(\frac{19\pi}{6}\); B) cos\(\frac{-11\pi}{3}\); г) tg \(\frac{11\pi}{6}\); Д) ctg \(\frac{-13\pi}{4}\)

Ответ: a) \(-\frac{\sqrt{3}}{2}\); б) \(-\frac{1}{2}\); в) \(\frac{1}{2}\); г) \(-\frac{\sqrt{3}}{3}\); д) -1

a) cos 510° = cos (510° - 360°) = cos 150° = cos (180° - 30°) = -cos 30° = \(-\frac{\sqrt{3}}{2}\)

б) sin \(\frac{19\pi}{6}\) = sin (\(\frac{19\pi}{6}\) - 2\(\pi\)) = sin \(\frac{7\pi}{6}\) = sin (\(\pi + \frac{\pi}{6}\)) = -sin \(\frac{\pi}{6}\) = \(-\frac{1}{2}\)

в) cos \(\frac{-11\pi}{3}\) = cos \(\frac{11\pi}{3}\) = cos (\(\frac{11\pi}{3}\) - 2\(\pi\)) = cos \(\frac{5\pi}{3}\) = cos (2\(\pi - \frac{\pi}{3}\)) = cos \(\frac{\pi}{3}\) = \(\frac{1}{2}\)

г) tg \(\frac{11\pi}{6}\) = tg (2\(\pi - \frac{\pi}{6}\)) = -tg \(\frac{\pi}{6}\) = \(-\frac{\sqrt{3}}{3}\)

д) ctg \(\frac{-13\pi}{4}\) = -ctg \(\frac{13\pi}{4}\) = -ctg (3\(\pi + \frac{\pi}{4}\)) = -ctg (\(\pi + \frac{\pi}{4}\)) = -ctg \(\frac{\pi}{4}\) = -1

Ответ: a) \(-\frac{\sqrt{3}}{2}\); б) \(-\frac{1}{2}\); в) \(\frac{1}{2}\); г) \(-\frac{\sqrt{3}}{3}\); д) -1