Question

СРОЧНО ДАЮ 100 БАЛЛОВ
2sin²x + 5sinx + 2 = 0

Answer 1

$2\sin^2x+5\sin x+2=0\\D_{\sin x}=25-16=9\Rightarrow \sin x=\cfrac{-5\pm \sqrt{9}}{4}=\left \{ -2,-\cfrac{1}{2} \right \}\\\sin x=-\frac{1}{2}\Rightarrow x=\left \{ -\cfrac{\pi}{6}+2\pi k, -\cfrac{5\pi}{6}+2\pi k \right \},k\in \mathbb{Z}$