Question

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

Answer 1

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