Question

The domain of the function $\sqrt{\sin 2x}$ is

• A. $\cup [n\pi -\frac{\pi }{2},n\pi ],n\in Z$
• B. $\cup [n\pi ,n\pi +\frac{\pi }{2}],n\in Z$
• C. $\cup \left[\right(2n-1)\pi ,2n\pi ],n\in Z$
• D. $\cup [2n\pi ,(2n+1\left)\pi \right],n\in Z$

Answer 1

The correct option is B $\cup [n\pi ,n\pi +\frac{\pi }{2}],n\in Z$

For $\sqrt{\sin 2x}$ to be defined,
$\sin 2x\ge 0$
$2x\in [2n\pi ,(2n+1\left)\pi \right]$
$\therefore x\in \cup [n\pi ,n\pi +\frac{\pi }{2}],n\in Z$