AMC 12 2009b Problem 24

For how many values of $x$ in $[0,\pi]$ is $\sin^{ - 1}(\sin 6x) = \cos^{ - 1}(\cos x)$? Note: The functions $\sin^{ - 1} = \arcsin$ and $\cos^{ - 1} = \arccos$ denote inverse trigonometric functions.

\textbf{(A)}\ 3 \textbf{(B)}\ 4 \textbf{(C)}\ 5 \textbf{(D)}\ 6 \textbf{(E)}\ 7