Answer
The exact value of the provided expression is $1$.
Work Step by Step
Let us assume $\theta ={{\cos }^{-1}}\left( 0 \right)$. Then, we have
$\cos \theta =0$
We know that for the cosine function, the interval for the angle is $\left[ 0,\pi \right]$.
Therefore, the only angle that satisfies $\cos \theta =0$ is $\frac{\pi }{2}$.
Hence, $\theta =\left( \frac{\pi }{2} \right)$ and the exact value of the given expression is
$\begin{align}
& \sin \left( {{\cos }^{-1}}0 \right)=\sin \left( \theta \right) \\
& =\sin \left( \frac{\pi }{2} \right) \\
& =1
\end{align}$
