Find the exact function value.
-$\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$
A) $\frac { 2 \pi } { 3 }$
B) $\frac { 3 \pi } { 4 }$
C) $\frac { \pi } { 4 }$
D) $\frac { \pi } { 3 }$

Question

Quizplus · Accepted Answer

The inverse sine function returns the angle whose sine is equal to the input. In this case, we are looking for the angle whose sine is equal to $\frac{\sqrt{3}}{2}$. From the unit circle, we know this occurs at $\frac{\pi}{3}$. However, since we are using the inverse sine function, we need to specify the angle in the appropriate range. Since $\sin(\frac{2\pi}{3}) = \frac{\sqrt{3}}{2}$ and that is larger than $\frac{\pi}{3}$, we know the answer must be $\frac{\pi}{3}$ or larger. Since $\sin(\frac{3\pi}{4})$ and $\sin(\pi - \frac{\pi}{3})$ equal $\frac{\sqrt{2}}{2}$, $\frac{\pi}{6}$ is too small, and the answer must be $\boxed{	ext{(D)}}$.

Find the Exact Function Value sin⁡−1(32)\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)sin−1(23​​)

Find the Exact Function Value $\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$