Question

Графически решить неравенство

Квадратный корень из 2 sin x <или= 1

Answer 1

$sqrt{2sin x } le 1 \ \ left{ begin{gathered} 2sin x ge 0 \ 2sin x le 1 \ end{gathered} ; left{ begin{gathered} sin x ge 0 \ sin x le dfrac{1}{2} \ end{gathered} right. right.$

$left{ begin{gathered} x ge pi n,n in Z \ left[ begin{gathered} x le dfrac{pi}{6} + 2pi n, n in Z \ x le dfrac{5pi}{6} + 2pi n,n in Z \ end{gathered} right. end{gathered} right. (1)$

$xin [pi ; dfrac{5pi}{6}] cup [dfrac{pi}{6};0] + 2pi n, n in Z$

Ответ: x ∈ [π; 5π/6] ∪ [π/6; 0] + 2πn, n ∈ Z