Answer
false
Work Step by Step
RECALL:
For $\arcsin{x}$, the value of $x$ must be $-\frac{\pi}{2}\lt x \lt \frac{\pi}{2}$
Thus, $\arcsin{(-\frac{1}{2})}\ne \frac{11\pi}{6}$ since it is not within the range of arcsin. In fact, $\arcsin{(-\frac{1}{2})}=-\frac{\pi}{6}$
Therefore, the given statement is false.
