3.1. Приведите тригонометрическую функцию произвольного аргумента к тригонометрической функции острого угла: \(\sin 340^\circ\), \(\cos(-\frac{11\pi}{9})\), \(tg(-523^\circ)\), \(ctg \frac{18\pi}{7}\)

1) \(\sin 340^\circ = \sin (360^\circ - 20^\circ) = -\sin 20^\circ\) 2) \(\cos(-\frac{11\pi}{9}) = \cos(\frac{11\pi}{9}) = \cos(\pi + \frac{2\pi}{9}) = -\cos(\frac{2\pi}{9})\) 3) \(tg(-523^\circ) = -tg(523^\circ) = -tg(360^\circ + 163^\circ) = -tg(163^\circ) = -tg(180^\circ - 17^\circ) = tg(17^\circ)\) 4) \(ctg\frac{18\pi}{7} = ctg(2\pi + \frac{4\pi}{7}) = ctg\frac{4\pi}{7} = ctg(\pi - \frac{3\pi}{7}) = -ctg\frac{3\pi}{7}\) Ответ: \(-\sin 20^\circ\), \(-\cos(\frac{2\pi}{9})\), \(tg(17^\circ)\), \(-ctg\frac{3\pi}{7}\)