Question

What is the domain of arcsin(Sin(x))?

Answer 1

Answer on Question #52804 – Math – Real Analysis

Question

What is the domain of $arcsin(\sin x)$?

Solution

The domain of $\sin x$ is $\mathbb{R}$ (the set of real numbers), the range of $\sin x$ is $[-1; 1]$, because $\sin x$ takes on values from $[-1; 1]$ for every real $x$. The domain of $arcsin(t)$ is $[-1; 1]$, denote $t = \sin x$ and obtain that $arcsin(\sin x)$ is correct for every real number $x$.

Thus, the domain of $arcsin(\sin x)$ is $\mathbb{R}$ (the set of real numbers).

Answer: $\mathbb{R}$.

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