# How do you find the exact value of arcsin(-sqrt3)?

Recall the Definition of $a r c \sin$ fun :
$a r c \sin x = \theta , x \in \left[- 1 , 1\right] \iff \sin \theta = x , \theta \in \left[- \frac{\pi}{2} , \frac{\pi}{2}\right] .$
Now, since $- \sqrt{3} \notin \left[- 1 , 1\right] , a r c \sin \left(- \sqrt{3}\right)$ is undefined.