# What is arcsin 0?

Jul 2, 2015

$\arcsin 0 = 0$

#### Explanation:

$\arcsin x$ is a $\theta$ with $\theta$ between $- \frac{\pi}{2}$ and $\frac{\pi}{2}$ (between $- {90}^{\circ}$ and ${90}^{\circ}$) with $\sin \theta = x$

So, $a r c \sin 0$ is an number (an angle) in the correct range, with $\sin \theta = 0$

The angles with sine = 0 are co-terminal with $0$ or with $\pi$ (in degrees, with ${180}^{\circ}$)

The only such angle between $- \frac{\pi}{2}$ and $\frac{\pi}{2}$ is the angle $\theta = 0$.

So $\arcsin 0 = 0$ (Either the number $0$ or the angle measuring $0$ radians or ${0}^{\circ}$ depending on the units of the application.)