Answer
$See$ $table$ $of$ $values$ $below$ $for$ $y$ $=$ $\sin 2x$ $between$ $x = 0$ $and$ $x = 2\pi$:
$x = 0$ $;$ $y = 0$
$x = \frac{\pi}{4}$ $;$ $y = 1$
$x = \frac{\pi}{2}$ $;$ $y = 0$
$x = \frac{3\pi}{4}$ $;$ $y =-1$
$x = \pi$ $;$ $y = 0$
$x = \frac{5\pi}{4}$ $;$ $y = 1$
$x = \frac{3\pi}{2}$ $;$ $y = 0$
$x = \frac{7\pi}{4}$ $;$ $y = -1$
$x = 2\pi$ $;$ $y = 0$
$There$ $are$ $2$ $complete$ $cycles$ $between$ $x = 0$ $and$ $x = 2\pi$:
Work Step by Step
$See$ $graph$ $below$ $for$ $y$ $=$ $\sin 2x$ $between$ $x = 0$ $and$ $x = 2\pi$:
