Question

The period of the function $y={\sin }^{-1}\left(\sin x\right)$ is

• A. $2\pi$
• B. $4\pi$
• C. $3\pi$
• D. $1\pi$

Answer 1

The correct option is A $2\pi$

Given, $f\left(x\right)={\sin }^{-1}\left(\sin x\right)$

Domain of $f\left(x\right)$ is $R$ and $\sin x$ is periodic. Hence $f\left(x\right)={\sin }^{-1}\left(\sin x\right)$ is also periodic. Here, we can make use of the graph to visualise the periodicity of the function.
Since, $\sin \left(x\right)$ has a period of $2\pi ,{\sin }^{-1}\left(\sin x\right)$ also has a period of $2\pi$. The graph below shows the functions $y={\sin }^{-1}\left(\sin x\right)$ and $y=\sin x$