Question

Решить уравнение:
$2sin(-\frac{x}{3})=\sqrt{2}$

Answer 1

$2Sin(-\frac{x}{3})=\sqrt{2}\\\\Sin(-\frac{x}{3})=\frac{\sqrt{2}}{2}\\\\-\frac{x}{3}=(-1)^{n}arcSin\frac{\sqrt{2}}{2}+\pi n,n\in Z\\\\-\frac{x}{3}=(-1)^{n}\frac{\pi}{4}+\pi n,n\in Z\\\\x=(-1)^{n+1}\frac{3\pi}{4}-3\pi n,n\in Z$