Question

If 'n' is an integer, the domain of the function $\sqrt{\sin 2x}$ is

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

Answer 1

Answer: (B)

$\left[n\pi, n\pi+\frac{\pi}{2}\right]$

Answer 2

The function is defined when $\sin 2x \ge 0$. This occurs when $2k\pi \le 2x \le (2k+1)\pi$, where $k$ is an integer. Dividing by 2, we get $k\pi \le x \le k\pi + \frac{\pi}{2}$. Replacing $k$ with $n$, the domain is $\left[n\pi, n\pi + \frac{\pi}{2}\right]$.