12. \( \cos(-500^\circ), \sin(\frac{12\pi}{7}), tg(-361^\circ), ctg(\frac{16\pi}{3}) \)

* \( \cos(-500^\circ) = \cos 500^\circ = \cos(360^\circ + 140^\circ) = \cos 140^\circ = \cos(180^\circ - 40^\circ) = -\cos 40^\circ \) * \( \sin(\frac{12\pi}{7}) = \sin(\pi + \frac{5\pi}{7}) = -\sin(\frac{5\pi}{7}) = -\sin(\pi - \frac{2\pi}{7}) = -\sin(\frac{2\pi}{7}) \) * \( tg(-361^\circ) = -tg 361^\circ = -tg(360^\circ + 1^\circ) = -tg 1^\circ \) * \( ctg(\frac{16\pi}{3}) = ctg(5\pi + \frac{\pi}{3}) = ctg(\pi + \frac{\pi}{3}) = ctg(\frac{\pi}{3}) \)