Question

The period of the function $f(x)=|\sin x|+|\cos x|$ is:

• A. $2\pi$
• B. $3\pi$
• C. $\frac{3\pi }{2}$
• D. $\pi$
• E. $\frac{\pi }{2}$

Answer 1

Answer: (D)

$|\sin x|$ and $|\cos x|$ are periodic functions with period $\pi$ . $\therefore$ $|\sin x|+|\cos x|$ is periodic with period is the LCM Of $(\pi ,\pi )=\pi$ $\therefore$ Period of $|\sin x|+|\cos x|=\pi$ .