Inverse functions when will $\sin(\arcsin x)$ be defined

Question

So first i know $\sin(x)$ has a domain of $\mathbb{R}$ and a codmain of $[-1,1]$ while the $\arcsin(x)$ is the opposite, domain of $[-1,1]$ with a codmain of $\mathbb{R}$. So $\sin(\arcsin(x)) = x$. But will $ \sin(\arcsin(10)) = 10$? I would like to think no because $10$ is not in the domain of $\arcsin(x)$. But using the identity it is equal to $10$. Can someone help me understand which logic is correct?

Answer 1

The equality is only true on the proper domain of $\sin$ and $\arcsin.$

Answer 2

Since $\arcsin 10$ is not defined, neither is $\sin (\arcsin 10)$.