Find the exact value of the expression below.
$\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]$
A) $\frac { 7 \pi } { 2 }$
B) $- \pi$
C) $- \frac { \pi } { 2 }$
D) $\frac { \pi } { 2 }$
E) $- \frac { 7 \pi } { 2 }$

Question

Quizplus · Accepted Answer

$\sin \left( \frac { 7 \pi } { 2 } ight) = \sin (\pi + \frac{\pi}{2}) = -1$. Therefore, $\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } ight) ight] = \sin ^ { - 1 } (-1)$. Using the fact that $\sin(\frac{-\pi}{2})=-1$, we see that $\sin ^ { - 1 } (-1) = \boxed{	extbf{(C) }- \frac { \pi } { 2 }}$.

Find the Exact Value of the Expression Below sin⁡−1[sin⁡(7π2)]\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]sin−1[sin(27π​)]

Find the Exact Value of the Expression Below $\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]$