Amplitude and period

Compare the graph of $y = 2\sin 2x$ with the basic $y = \sin x$. In general $y = a\sin bx$ has amplitude $|a|$ and period $\dfrac{2\pi}{b}$.

Here $a = 2$ and $b = 2$, so the amplitude is $2$ (values run from $-2$ to $2$) and the period is $\dfrac{2\pi}{2} = \pi$ (one cycle every $\pi$). Compared with $y = \sin x$ (amplitude $1$, period $2\pi$), it is stretched twice as tall and squeezed to half the width. The large dots are the maximum of $2\sin 2x$ at $\left(\dfrac{\pi}{4}, 2\right)$ and of $\sin x$ at $\left(\dfrac{\pi}{2}, 1\right)$.