$\begin{array}{l}
\sqrt {3 + {{\sin }^{2018}}x} \\
- 1 \le \sin x \le 1\\
\Rightarrow 0 \le {\sin ^{2018}}x \le 1\\
\Rightarrow 3 \le 3 + {\sin ^{2018}}x \le 4\\
\Rightarrow \sqrt 3 \le \sqrt {3 + {{\sin }^{2018}}x} \le 2\\
\to \max y = 2\\
\Rightarrow {\sin ^{2018}}x = 1\\
\Rightarrow \sin x = \pm 1\\
\Rightarrow x = \frac{\pi }{2} + k\pi \left( {k \in Z} \right)\\
\to \min y = \sqrt 3 \\
\Rightarrow \sin x = 0 \Rightarrow x = k\pi \left( {k \in Z} \right)
\end{array}$
