Answer
The graph of
$x=sin~t$
$y=sin(2t)$
Work Step by Step
Some important points to sketch the graph:
$t=0$:
$x=0$
$y=0$
The graph passes through the origin.
$t=\frac{\pi}{4}$:
$x=\frac{\sqrt 2}{2}$
$y=1$
The "top" at the right side.
$t=\frac{\pi}{2}$:
$x=1$
$y=0$
The graph passes through the positive x-axis.
$t=\frac{3\pi}{4}$:
$x=\frac{\sqrt 2}{2}$
$y=-1$
The "bottom" at the right side.
$t=\pi$:
$x=0$
$y=0$
The graph passes through the origin.
$t=\frac{5\pi}{4}$:
$x=-\frac{\sqrt 2}{2}$
$y=1$
The "top" at the left side.
$t=\frac{3\pi}{2}$:
$x=-1$
$y=0$
The graph passes through the negative x-axis.
$t=\frac{7\pi}{4}$:
$x=\frac{\sqrt 2}{2}$
$y=-1$
The "bottom" at the left side.
