2. Решите неравенства a) sin(x/2)≥(√2)/2 б) cos 3x ≥ (√3)/2

2. Решите неравенства

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

$$\frac{x}{2} \in [\frac{\pi}{4} + 2\pi n; \frac{3\pi}{4} + 2\pi n], n \in Z$$

$$x \in [\frac{\pi}{2} + 4\pi n; \frac{3\pi}{2} + 4\pi n], n \in Z$$

б) $$cos(3x) \ge \frac{\sqrt{3}}{2}$$

$$3x \in [-\frac{\pi}{6} + 2\pi n; \frac{\pi}{6} + 2\pi n], n \in Z$$

$$x \in [-\frac{\pi}{18} + \frac{2\pi n}{3}; \frac{\pi}{18} + \frac{2\pi n}{3}], n \in Z$$

Ответ:

a) $$x \in [\frac{\pi}{2} + 4\pi n; \frac{3\pi}{2} + 4\pi n], n \in Z$$

б) $$x \in [-\frac{\pi}{18} + \frac{2\pi n}{3}; \frac{\pi}{18} + \frac{2\pi n}{3}], n \in Z$$