Chapter 7, Problem 9RE

Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.� Do not use a calculator.

${\sin }^{-1}\left(\sin \frac{3\pi }{8}\right)$

To determine

To find: The exact value of expression ${\sin }^{-1}\sin \frac{3\pi }{8}$.

Answer to Problem 9RE

The exact value of expression ${\sin }^{-1}\sin \frac{3\pi }{8}=\frac{3\pi }{8}$.

Explanation of Solution

Given:

${\sin }^{-1}\sin \frac{3\pi }{8}$

Calculation:

Let $A={\sin }^{-1}\sin \frac{3\pi }{8}$,

$\sin A=\sin \frac{3\pi }{8}$

$A=\frac{3\pi }{8}$

Value of ${\sin }^{-1}\sin \frac{3\pi }{8}$ is $\frac{3\pi }{8}$.