2. Решите неравенства a) sin 4x≥-1/2 6) cos(x/9)≥-(√2)/2

Решение неравенств:

a) $$sin(4x) \ge -\frac{1}{2}$$

$$4x \in [-\frac{\pi}{6} + 2\pi n; \frac{7\pi}{6} + 2\pi n], n \in Z$$

$$x \in [-\frac{\pi}{24} + \frac{\pi n}{2}; \frac{7\pi}{24} + \frac{\pi n}{2}], n \in Z$$

б) $$cos(\frac{x}{9}) \ge -\frac{\sqrt{2}}{2}$$

$$\frac{x}{9} \in [-\frac{3\pi}{4} + 2\pi n; \frac{3\pi}{4} + 2\pi n], n \in Z$$

$$x \in [-\frac{27\pi}{4} + 18\pi n; \frac{27\pi}{4} + 18\pi n], n \in Z$$

Ответ:

a) $$x \in [-\frac{\pi}{24} + \frac{\pi n}{2}; \frac{7\pi}{24} + \frac{\pi n}{2}], n \in Z$$

б) $$x \in [-\frac{27\pi}{4} + 18\pi n; \frac{27\pi}{4} + 18\pi n], n \in Z$$