Answer
$a.\displaystyle \quad -\frac{\pi}{6}$
$b.\displaystyle \quad\frac{\pi}{4}$
$c.\displaystyle \quad -\frac{\pi}{3}$
Work Step by Step
$y=\sin^{-1}x$ is the number in $[-\pi/2, \pi/2]$ for which $\sin y=x.$
Use reference angles in the 1st quadrant,
keeping in mind that sine is an odd function.
$\left\{\begin{array}{llll}
\sin\frac{\pi}{6}=\frac{1}{2} & \Rightarrow & \sin(-\frac{\pi}{6})=-\dfrac{1}{2} & \sin^{-1}(-\frac{1}{2})=-\frac{\pi}{6}\\
& & & \\
\sin\frac{\pi}{4}=\frac{1}{\sqrt{2}} & \Rightarrow & & \sin^{-1}(\frac{1}{\sqrt{2}})=\dfrac{\pi}{4}\\
& & & \\
\sin\frac{\pi}{3}=\frac{ \sqrt{3}}{2} & \Rightarrow & \sin(-\frac{\pi}{3})=-\frac{\sqrt{3}}{2} & \Rightarrow\sin^{-1}(-\frac{\sqrt{3}}{2})=-\dfrac{\pi}{3}
\end{array}\right.$
