Q. The period of the function $f(x) = \sin\left( \sin\frac{x}{5} \right)$ is
A) 2$\pi$
B) 2$\pi/5$
C) 10$\pi$
D) 5$\pi$
Explanation
(c)
$\ \ \ \ \ \ \ f(x + 10\pi) = \sin\left\{ \sin\left( \frac{x + 10\pi}{5} \right) \right\}$
$\Rightarrow \ f(x + 10\pi) = \sin\left\{ \sin\left( \frac{x}{5} + 2\pi \right) \right\}$
$\Rightarrow \ f(x + 10\pi) = \sin{\left\{ \sin\left( \frac{x}{5} \right) \right\} = f(x)}$
Therefore, period of $f(x)$ is $10\pi$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.