Question

resolva no intervalo 0 ≤ x 2π na equação sen^3x-senx=0

Answer 1

Olá, Gordaaoo.

$\sin^3x-\sin x=0\Rightarrow\,(\sin x)(\sin^2x-1)=0\Rightarrow \begin{cases}\sin x=0\\\sin^2x-1=0\end{cases}\Rightarrow\\\\\\ \begin{cases}\sin x=0\Rightarrow\boxed{x=0}\text{ ou }\boxed{x=\pi}\\\sin^2x=1\Rightarrow\sin x=\sqrt1\Rightarrow\sin x=\pm1\Rightarrow \boxed{x=\pm\frac{\pi}2}\end{cases}$

Conjunto-solução: $\boxed{S=\left\{0,\pm\frac{\pi}2,\pi\right\}}$