Question

em quantos quadrantes aparecem as soluções da inequação -1<2sen x <√3
a) 1
b) 2
c) 3
d) 4​

Answer 1

$\mathsf{-1\textless 2sen(x)\textless\sqrt{3}}\\\implies\begin{cases}\mathsf{2sen(x)>-1}\\\mathsf{2sen(x)\textless\sqrt{3}}\end{cases}$

$\mathsf{2sen(x)>-1}\\\mathsf{sen(x)>-\dfrac{1}{2}}\\\mathsf{\dfrac{7\pi}{6}\textless x\textless\dfrac{\</p><p>3\pi}{2}~~ou~~\dfrac{11\pi}{6}\textless x\textless2\pi}$

$\mathsf{2sen(x)\textless\sqrt{3}}\\\mathsf{sen(x)\textless\dfrac{\sqrt{3}}{2}}\\\mathsf{0\textless x\textless\dfrac{\pi}{3}~~ou~~\dfrac{\pi}{2}\textless x\textless\dfrac{2\pi}{3}}$

Aparecem nos quatro quadrantes.

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\maltese~~alternativa~~d}}}}}$