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

$\sin \left( \frac { 7 \pi } { 2 } \right)$ is equivalent to $\sin \left( 2\pi + \frac { \pi } { 2 } \right)$, which simplifies to $\sin \left( \frac { \pi } { 2 } \right) = 1$. The value of $\sin ^ { - 1 } (1)$ is $\frac { \pi } { 2 }$, but since the range of the arcsin function is $[- \frac { \pi } { 2 }, \frac { \pi } { 2 }]$, the correct answer is $\frac { \pi } { 2 }$.

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 $\sin ^ { - 1 } \left[ \sin \left( \frac { 7 \pi } { 2 } \right) \right]$