$\begin{array}{l}
\sin x = \dfrac{1}{2}\\
\Leftrightarrow \sin x = \sin \dfrac{\pi }{6}\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{6} + k2\pi \\
x = \pi - \dfrac{\pi }{6} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{6} + k2\pi \\
x = \dfrac{{5\pi }}{6} + k2\pi
\end{array} \right.\left( {k \in \mathbb{Z}} \right)
\end{array}$
