Find the exact value of the expression. Do not use a calculator.
-$$\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]$$
A) $5 \pi$
B) $\frac { \pi } { 5 }$
C) $- 5 \pi$
D) $- \frac { \pi } { 5 }$

Question

Quizplus · Accepted Answer

The expression $\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]$ simplifies directly to $\frac { \pi } { 5 }$ because $\sin ^ { - 1 }$ and $\sin$ are inverse functions, and $\frac { \pi } { 5 }$ is within the domain of the arcsin function $[- \frac{\pi}{2}, \frac{\pi}{2}]$.

Find the Exact Value of the Expression sin⁡−1[sin⁡(π5)]\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]sin−1[sin(5π​)]

Find the Exact Value of the Expression $\sin ^ { - 1 } \left[ \sin \left( \frac { \pi } { 5 } \right) \right]$