Answer
$-\dfrac{ \pi}{10}$
Work Step by Step
Value of certain composite functions formula:
$f^{-1}(f(x)= \sin^{-1}{(\sin{x})} = x \hspace{25pt} -\dfrac{\pi}{2}\leq x \leq \dfrac{\pi}{2}$
Thus,
$\sin^{-1} {\left[\sin{\left(-\dfrac{ \pi}{10} \right)} \right]} = -\dfrac{ \pi}{10}$
