2. Решите неравенства и найдите значения неизвестной a) sin x ≥ -\frac{\sqrt{2}}{2} б) cos 4x ≤ \frac{\sqrt{3}}{2}

a) $$sin x \ge -\frac{\sqrt{2}}{2}$$

$$x \in [-\frac{\pi}{4}+2\pi n; \frac{5\pi}{4}+2\pi n], n \in Z$$

б) $$cos 4x \le \frac{\sqrt{3}}{2}$$

$$4x \in [\frac{\pi}{6}+2\pi n; \frac{11\pi}{6}+2\pi n], n \in Z$$

$$x \in [\frac{\pi}{24}+\frac{\pi n}{2}; \frac{11\pi}{24}+\frac{\pi n}{2}], n \in Z$$

Ответ: a) $$x \in [-\frac{\pi}{4}+2\pi n; \frac{5\pi}{4}+2\pi n], n \in Z$$; б) $$x \in [\frac{\pi}{24}+\frac{\pi n}{2}; \frac{11\pi}{24}+\frac{\pi n}{2}], n \in Z$$