Question

Determine o conjunto solução das seguintes
equações:
A) a) 2 sen x + 1 = 0
B) 2 sen 2x = 1
se alguem puder responder, obrigado.

Answer 1

$\large\boxed{\begin{array}{l}\rm a)~\sf 2sen(x)+1=0\\\sf 2sen(x)=-1\\\sf sen(x)=-\dfrac{1}{2}\\\sf x=\dfrac{7\pi}{6}+2k\pi,k\in\mathbb{Z}\\\\\sf ou\\\\\sf x=\dfrac{11\pi}{6}+2k\pi,k\in\mathbb{Z}\end{array}}$

$\large\boxed{\begin{array}{l}\rm b)~\sf 2sen(2x)=1\\\sf sen(2x)=\dfrac{1}{2}\\\\\sf 2x=\dfrac{\pi}{6}+2k\pi\\\\\sf x=\dfrac{1}{2}\bigg[\dfrac{\pi}{6}+2k\pi\bigg]\\\\\sf x=\dfrac{\pi}{12}+k\pi,k\in\mathbb{Z}\\\sf ou\\\sf 2x=\dfrac{5\pi}{6}+2k\pi\\\\\sf x=\dfrac{1}{2}\bigg[\dfrac{5\pi}{6}+2k\pi\bigg]\\\\\sf x=\dfrac{5\pi}{12}+k\pi,k\in\mathbb{Z}\end{array}}$