Question

Решите уравнение sin(пx/8)=-1/корень из 2

Answer 1

$sin\frac{\pi x}{8}=-\frac{1}{\sqrt2}\\\\\frac{\pi x}{8}=(-1)^{n}\cdot arcsin(-\frac{1}{\sqrt2})+\pi n,\\\\\frac{\pi x}{8}=(-1)^{n+1}\cdot \frac{\pi}{4}+\pi n,\\\\x=(-1)^{n+1}\cdot 2+8n,\; n\in Z$