Use the properties of inverse trigonometric functions to evaluate $\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]$.
A) $- \frac { 5 \pi } { 9 }$
B) $\frac { 4 \pi } { 5 }$
C) $\frac { 9 \pi } { 4 }$
D) $\frac { 4 \pi } { 9 }$
E) $\frac { \pi } { 9 }$

Question

Quizplus · Accepted Answer

The function $\arcsin(\sin(x))$ returns the original value of $x$ if $x$ is in the domain of the arcsine function, which is $[- \frac{\pi}{2}, \frac{\pi}{2}]$. Since $\frac{4\pi}{9}$ is within this interval, $\arcsin(\sin(\frac{4\pi}{9})) = \frac{4\pi}{9}$.

Use the Properties of Inverse Trigonometric Functions to Evaluate arcsin⁡[sin⁡(4π9)]\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]arcsin[sin(94π​)]

Use the Properties of Inverse Trigonometric Functions to Evaluate $\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]$