29.5. Решите уравнение: 1) sin x - π = √2; ( 6 2 3) √2 sin π - 3x - 1 = 0. 12 ( 2) sin x +1 = -1;

29.5. Решите уравнение:

1) $$sin(x - \frac{\pi}{6}) = \frac{\sqrt{2}}{2}$$

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

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

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

2) $$sin(\frac{x}{3} + 1) = -1$$

$$\frac{x}{3} + 1 = -\frac{\pi}{2} + 2\pi n, n \in Z$$

$$\frac{x}{3} = -1 - \frac{\pi}{2} + 2\pi n, n \in Z$$

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

Ответ: $$x = -3 - \frac{3\pi}{2} + 6\pi n, n \in Z$$

3) $$\sqrt{2}sin(\frac{\pi}{12} - 3x) - 1 = 0$$

$$sin(\frac{\pi}{12} - 3x) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$$

$$\frac{\pi}{12} - 3x = (-1)^n \frac{\pi}{4} + \pi n, n \in Z$$

$$-3x = (-1)^n \frac{\pi}{4} - \frac{\pi}{12} + \pi n, n \in Z$$

$$x = (-1)^{n+1} \frac{\pi}{12} + \frac{\pi}{36} - \frac{\pi n}{3}, n \in Z$$

Ответ: $$x = (-1)^{n+1} \frac{\pi}{12} + \frac{\pi}{36} - \frac{\pi n}{3}, n \in Z$$