Chapter 7.1, Problem 52AYU

To determine

To find: The exactvalue of the composite function.

Answer to Problem 52AYU

The exact value of $\sin \left[{\sin }^{-1}\left(-1.5\right)\right]$ is $-1.5$.

Explanation of Solution

Given:

  $\sin \left[{\sin }^{-1}\left(-1.5\right)\right]$

The exact value of $\sin \left[{\sin }^{-1}\left(-1.5\right)\right]$ is

  $\begin{array}{l}\sin \left[{\sin }^{-1}\left(-1.5\right)\right]\\ =\sin \left({\sin }^{-1}\right)\left(-1.5\right)\\ =-1.5\end{array}$

Hence, the exact value of $\sin \left[{\sin }^{-1}\left(-1.5\right)\right]$ is $-1.5$.