Question

resolva a equação:4sen²x-3=0​

Answer 1

$\boxed{\begin{array}{l}\sf4sen^2(x)-3=0\\\sf 4sen^2(x)=3\\\sf sen^2(x)=\dfrac{3}{4}\\\sf sen(x)=\pm\dfrac{\sqrt{3}}{\sqrt{4}}\\\sf sen(x)=\pm\dfrac{\sqrt{3}}{2}\\\sf sen(x)=\dfrac{\sqrt{3}}{2}\\\sf x=\dfrac{\pi} {3}+2k\pi,k\in\mathbb{Z} ~~x=\dfrac{2\pi}{3}+2k\pi,k\in\mathbb{Z}\\\sf sen(x)=-\dfrac{\sqrt{3}}{2}\\\sf x=\dfrac{4\pi}{3}+2k\pi,k\in\mathbb{Z}~~ x=\dfrac{5\pi}{3}+2k\pi,k\in\mathbb{Z}\end{array}}$

$\sf S=\bigg\{\dfrac{\pi}{3}+2k\pi,k\in\mathbb{Z}, \dfrac{2\pi}{3}+2k\pi,k\in\mathbb{Z},\dfrac{5\pi} {3}+2k\pi,k\in\mathbb{Z},\dfrac{5\pi}{3}+2k\pi, k\in\mathbb{Z} \bigg\}$