Compute $\arcsin 0.$  Express your answer in radians.
Since $\sin 0 = 0,$ $\arcsin 0 = \boxed{0}.$
0
Level 1
Precalculus
Problem: Compute $\arcsin 0.$  Express your answer in radians.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To compute $\arcsin 0$, we need to understand the definition of the arcsine function. The arcsine function, $\arcsin x$, is the inverse of the sine function, defined for $x$ in the range $[-1, 1]$. The output of $\arcsin x$ is an angle $\theta$ such that $\sin \theta = x$ and $\theta$ is restricted to the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.

In this case, we are looking for an angle $\theta$ such that $\sin \theta = 0$. The sine function equals zero at integer multiples of $\pi$, specifically at $\theta = n\pi$ for any integer $n$. However, since we are restricted to the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, we need to find the specific value of $n$ that falls within this range.

The only integer multiple of $\pi$ that lies within the interval $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is $0$. Therefore, we conclude that $\theta = 0$ is the only solution that satisfies both the equation $\sin \theta = 0$ and the range restriction of the arcsine function.

Thus, the final answer is $0$.<|END_OF_LATENT|> The final answer is $0$.