Question

The period of the function $f\left(x\right)=\sin \left(\sin \frac{x}{5}\right)$ is

• A. $2\pi$
• B. $2\pi /5$
• C. $10\pi$
• D. $5\pi$

Answer 1

The correct option is C $10\pi$

Period of $sin\left(\frac{x}{5}\right)=2\pi \times 5=10\pi$
$\therefore f\left(x\right)=sin\left(sin\frac{x}{5}\right)$
Quantity inside function sin varies with period of $10\pi$.
So, that period of $sin\left(sin\frac{x}{5}\right)=10\pi$
Concept - If $f\left(x\right)$ is a Periodic function with Period $T$ and $g\left(x\right)$ is any function such that range if $f$ is a proper subset of the domain if $g$, then $g\left(f\right(x\left)\right)$ is Periodic with Period $T$.