1) $$sinx = - \frac{\sqrt{2}}{2}$$

Решим уравнение $$sinx = - \frac{\sqrt{2}}{2}$$. $$x = arcsin(-\frac{\sqrt{2}}{2}) + 2\pi n, n \in Z$$ или $$x = \pi - arcsin(-\frac{\sqrt{2}}{2}) + 2\pi n, n \in Z$$ $$x = -\frac{\pi}{4} + 2\pi n, n \in Z$$ или $$x = \pi - (-\frac{\pi}{4}) + 2\pi n, n \in Z$$ $$x = -\frac{\pi}{4} + 2\pi n, n \in Z$$ или $$x = \frac{5\pi}{4} + 2\pi n, n \in Z$$ Ответ: $$x = -\frac{\pi}{4} + 2\pi n, x = \frac{5\pi}{4} + 2\pi n, n \in Z$$