The angle $\sin ^ { - 1 } \left( \sin \frac { 3 \pi } { 2 } \right)$ is

A) $- \frac { \pi } { 2 }$
B) $- \frac { 3 \pi } { 2 }$
C) $\frac { 3 \pi } { 2 }$
D) $- \frac { 9 \pi } { 2 }$
E) $\frac { 7 \pi } { 2 }$

Question

The angle $\sin ^ { - 1 } \left( \sin \frac { 3 \pi } { 2 } \right)$ is

A) $- \frac { \pi } { 2 }$
B) $- \frac { 3 \pi } { 2 }$
C) $\frac { 3 \pi } { 2 }$
D) $- \frac { 9 \pi } { 2 }$
E) $\frac { 7 \pi } { 2 }$

Quizplus · Accepted Answer

$\sin \frac { 3 \pi } { 2 }$ equals $-1$, and the angle whose sine is $-1$ within the domain of the arcsin function $[- \frac{\pi}{2}, \frac{\pi}{2}]$ is $- \frac { \pi } { 2 }$.

The Angle sin⁡−1(sin⁡3π2)\sin ^ { - 1 } \left( \sin \frac { 3 \pi } { 2 } \right)sin−1(sin23π​)

The Angle $\sin ^ { - 1 } \left( \sin \frac { 3 \pi } { 2 } \right)$