Đáp án:
$6$ nghiệm
Giải thích các bước giải:
$\sin x =\dfrac{\sqrt3}{2}$
$\Leftrightarrow \left[\begin{array}{l}x = \dfrac{\pi}{3} + k2\pi\\x = \dfrac{2\pi}{3} + k2\pi\end{array}\right.\quad (k\in \Bbb Z)$
Ta có:
$- 2\pi < x < 3\pi$
$\Leftrightarrow \left[\begin{array}{l}-2\pi< \dfrac{\pi}{3} + k2\pi< 3\pi\\-2\pi< \dfrac{2\pi}{3} + k2\pi< 3\pi\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}-\dfrac{7}{6} < k < \dfrac{8}{6}\\-\dfrac{4}{3} < k < \dfrac{7}{6} \end{array}\right.$
$\Rightarrow \left[\begin{array}{l} k = \left\{-1;0;1\right\}\\k = \left\{-1;01\right\}\end{array}\right.$
$6$ giá trị $k \Rightarrow 6$ nghiệm
