Question

√2sin(x/3)=1 Помогите решить, очень срочно

Answer 1

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

$\frac{x}{3} = \arcsin(\frac{1}{\sqrt{2}}) + 2\pi m$

или

$\frac{x}{3} = \pi - \arcsin(\frac{1}{\sqrt{2}} + 2\pi n$

$\frac{x}{3} = \frac{\pi}{4} + 2\pi m$

или

$\frac{x}{3} = \pi - \frac{\pi}{4} + 2\pi n = \frac{3\pi}{4} + 2\pi n$

$x = \frac{3\pi}{4} + 6\pi m$

или

$x = \frac{9\pi}{4} + 6\pi n$

$n \in \mathbb{Z}$

$m \in \mathbb{Z}$