Question

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

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

Answer 1

The correct option is A $2\pi$

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