1. Вычислите: a) sin(13π/6); б) tg(-11π/6); в) cos(π) + ctg(4π/3); г) tg(π/4) * ctg(-π/4) + cos(3π/2) * sin(π/2); д) sin(405°) + cos(225°) * tg(225°);

a) \( sin(\frac{13\pi}{6}) \) = \( sin(2\pi + \frac{\pi}{6}) \) = \( sin(\frac{\pi}{6}) \) = \( \frac{1}{2} \) б) \( tg(-\frac{11\pi}{6}) \) = -\( tg(\frac{11\pi}{6}) \) = -\( tg(2\pi - \frac{\pi}{6}) \) = \( tg(\frac{\pi}{6}) \) = \( \frac{\sqrt{3}}{3} \) в) \( cos(\pi) + ctg(\frac{4\pi}{3}) \) = -1 + \( ctg(\pi + \frac{\pi}{3}) \) = -1 + \( ctg(\frac{\pi}{3}) \) = -1 + \( \frac{\sqrt{3}}{3} \) = \( \frac{\sqrt{3}-3}{3} \) г) \( tg(\frac{\pi}{4}) \cdot ctg(-\frac{\pi}{4}) + cos(\frac{3\pi}{2}) \cdot sin(\frac{\pi}{2}) \) = 1 \cdot (-1) + 0 \cdot 1 = -1 д) \( sin(405^\circ) + cos(225^\circ) \cdot tg(225^\circ) \) = \( sin(360^\circ + 45^\circ) + cos(180^\circ + 45^\circ) \cdot tg(180^\circ + 45^\circ) \) = \( sin(45^\circ) + cos(225^\circ) \cdot tg(225^\circ) \) = \( \frac{\sqrt{2}}{2} + (-\frac{\sqrt{2}}{2}) \cdot 1 \) = \( \frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2} \) = 0