Answer
The graph of $sin~6x$ with two periods is shown below.
Work Step by Step
The period of $sin~x$ is $2\pi$. We want two periods ($4\pi$). Then,
$0\lt6x\lt4\pi$
$0\lt x\lt\frac{2\pi}{3}$
Maximum:
$sin~6x=1$
$6x=\frac{\pi}{2}$ and $6x=\frac{5\pi}{2}$
$x=\frac{\pi}{12}$ and $x=\frac{5\pi}{12}$
Minimum:
$sin~6x=-1$
$6x=\frac{3\pi}{2}$ and $6x=\frac{7\pi}{2}$
$x=\frac{3\pi}{12}$ and $x=\frac{7\pi}{12}$
