Question

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

• A. $\mathrm{\pi }$
• B. $\frac{\mathrm{\pi }}{2}$
• C. $2\mathrm{\pi }$
• D. None of these

Answer 1

The correct option is B

$\frac{\mathrm{\pi }}{2}$

Explanation for the correct option:

Compute the period of the given function.

Given function, $f\left(x\right)=\left|\sin \left(x\right)\right|+\left|\cos \left(x\right)\right|$.

We know that the period of $\left|\sin \left(x\right)\right|$ is $\mathrm{\pi }$ and $\left|\cos \left(x\right)\right|$ is $\mathrm{\pi }$.

Then the period of $f\left(x\right)$ is given as $\frac{1}{2}\times$ (LCM of $\mathrm{\pi }$ and $\mathrm{\pi }$)$=\frac{\mathrm{\pi }}{2}$.

Hence, Option $\left(\mathrm{B}\right)$ is the correct answer.