Sine Function and Inverse Sine Function

For what value of $x$ does $\sin x={\sin }^{-1}x ?$

Sketch the graph of $y=\sin \left(\frac{1}{3}x\right)$ for $0\le x<6\mathrm{\pi }$.

Find all values of $x$ for $-8\mathrm{\pi }\le x\le 8\mathrm{\pi }$ and $\sin x=-1$.

Find all values of $x$ for $-10\mathrm{\pi }\le x\le 10\mathrm{\pi }$ and $\sin x=0$.