The expression $\sin^{-1}(0)$ asks for the angle whose sine value is $0$. The arcsine function, $\sin^{-1}$, is defined on the interval $[- \frac{\pi}{2}, \frac{\pi}{2}]$.

Solution:

The sine of $0$ is $0$. Therefore: $\sin^{-1}(0) = 0$

Correct Choice:

A. $\sin^{-1}(0) = 0$

This is the exact value. Let me know if you need more explanation!

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Related Questions to Explore:

1. What is $\sin^{-1}(1)$ and its exact value?
2. How is the domain of $\sin^{-1}$ defined?
3. What is the general solution for $\sin(x) = 0$?
4. Explain how to calculate $\cos^{-1}(0)$ and find its value.
5. Why is $\sin^{-1}(x)$ restricted to $[- \frac{\pi}{2}, \frac{\pi}{2}]$?

Tip:

When solving for $\sin^{-1}(x)$, always consider the range of the function: $[- \frac{\pi}{2}, \frac{\pi}{2}]$.