Q. The period of the function $f(x) = \left| \sin x \right| + |\cos x|$ is
A) $\pi$
B) $\pi/2$
C) $2\pi$
D) None of these
Explanation
(b)
$f\left( \frac{\pi}{2} + x \right) = \left| \sin\left( \frac{\pi}{2} + x \right) \right| + \left| \cos\left( \frac{\pi}{2} + x \right) \right|$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left| \cos x \right| + |\sin x|$ for all $x$.
Hence, $f(x)$ is periodic with period $\frac{\pi}{2}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.