Question

cossecante x = –√2 e π < x < 3π /2

Answer 1

Olá, Matheus.

$cossec\,x=\frac1{sen\,x}=-\sqrt2\Rightarrow sen\,x=-\frac1{\sqrt2}\Rightarrow \\\\ sen\,x=-\frac1{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=-\frac{\sqrt2}2\Rightarrow x=45\º+180\º=\frac\pi 4+\pi\ rad\\\\ \therefore \boxed{x=\frac{5\pi}4\ rad}$