\(\Leftrightarrow sin3x=\frac{\sqrt{3}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=\frac{\pi}{3}+k2\pi\\3x=\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{9}+\frac{k2\pi}{3}\\x=\frac{2\pi}{9}+\frac{k2\pi}{3}\end{matrix}\right.\)
Mà \(0\le x\le\pi\Rightarrow\left[{}\begin{matrix}0\le\frac{\pi}{9}+\frac{k2\pi}{3}\le\pi\\0\le\frac{2\pi}{9}+\frac{k2\pi}{3}\le\pi\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}-\frac{1}{6}\le k\le\frac{4}{3}\\-\frac{1}{3}\le k\le\frac{7}{6}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}k=\left\{0;1\right\}\\k=\left\{0;1\right\}\end{matrix}\right.\) \(\Rightarrow x=\left\{\frac{\pi}{9};\frac{7\pi}{9};\frac{2\pi}{9};\frac{8\pi}{9}\right\}\)
