Question

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

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

Answer 1

Answer: (A)

$\frac{\pi }{2}$

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

Now,

$f(\frac{\pi }{2}+x)=|\cos x|+|\sin x|=f\left(x\right)$.

So $\frac{\pi }{2}$ is the least number such that $f(\frac{\pi }{2}+x)=f\left(x\right)$.

So period of the function is $\frac{\pi }{2}$.