29.6. Решите уравнение: π 1) sin 8x = 1; 18 ( 2) 2sin x - 4 + 1 = 0. ( 5 )

29.6. Решите уравнение:

1) $$sin(\frac{\pi}{18} - 8x) = 1$$

$$\frac{\pi}{18} - 8x = \frac{\pi}{2} + 2\pi n, n \in Z$$

$$-8x = \frac{\pi}{2} - \frac{\pi}{18} + 2\pi n, n \in Z$$

$$-8x = \frac{9\pi}{18} - \frac{\pi}{18} + 2\pi n, n \in Z$$

$$-8x = \frac{8\pi}{18} + 2\pi n, n \in Z$$

$$x = -\frac{\pi}{18} - \frac{\pi n}{4}, n \in Z$$

Ответ: $$x = -\frac{\pi}{18} - \frac{\pi n}{4}, n \in Z$$

2) $$2sin(\frac{x}{5} - 4) + 1 = 0$$

$$sin(\frac{x}{5} - 4) = -\frac{1}{2}$$

$$\frac{x}{5} - 4 = (-1)^{n+1} \frac{\pi}{6} + \pi n, n \in Z$$

$$\frac{x}{5} = 4 + (-1)^{n+1} \frac{\pi}{6} + \pi n, n \in Z$$

$$x = 20 + (-1)^{n+1} \frac{5\pi}{6} + 5\pi n, n \in Z$$

Ответ: $$x = 20 + (-1)^{n+1} \frac{5\pi}{6} + 5\pi n, n \in Z$$