Question

The period of $|\sin 2x|$ is

• A. $\frac{\pi}{4}$
• B. $\frac{\pi}{2}$
• C. $\pi$
• D. $2\pi$

Answer 1

Answer: (B)

$\frac{\pi}{2}$

Answer 2

Here $|\sin 2x| = \sqrt{\sin^{2}2x} = \sqrt{\frac{(1 - \cos 4x)}{2}}$

Period of $\cos 4x$ is $\frac{\pi}{2}$. Hence, period of $|\sin 2x|$ will be $\frac{\pi}{2}$

Trick : $\because$ $\sin x$ has period $= 2\pi$ $\Rightarrow$ $\sin 2x$ has period $= \frac{2\pi}{2} = \pi$

Now, if $f(x)$ has period $p$ then $|f(x)|$ has period $\frac{p}{2}$

$\Rightarrow |\sin 2x|$ has period $= \frac{\pi}{2}.$