A2. Решите уравнение: a) sin(x/4) = √3/2; б) cos(x - π/3) = 1/2.

Решение:

• a) sin(x/4) = √3/2
  • \[ \frac{x}{4} = \frac{\pi}{3} + 2\pi k, \quad \frac{x}{4} = \frac{2\pi}{3} + 2\pi k, \quad k \in \mathbb{Z} \]
  • \[ x = \frac{4\pi}{3} + 8\pi k, \quad x = \frac{8\pi}{3} + 8\pi k, \quad k \in \mathbb{Z} \]
• б) cos(x - π/3) = 1/2
  • \[ x - \frac{\pi}{3} = \frac{\pi}{3} + 2\pi k, \quad x - \frac{\pi}{3} = -\frac{\pi}{3} + 2\pi k, \quad k \in \mathbb{Z} \]
  • \[ x = \frac{2\pi}{3} + 2\pi k, \quad x = 2\pi k, \quad k \in \mathbb{Z} \]