# How to plot the graph of f(x)=2 sin 4x?

Jul 22, 2015

Draw a standard $\sin$ curve but "squeeze" the vertical so the period is reduced from $2 \pi$ to $\frac{\pi}{2}$ and stretch the horizontal so the amplitude is increased from $\left[- 1 , 1\right]$ to $\left[- 2 , 2\right]$

#### Explanation:

$\sin \left(\theta\right)$ has a period of $2 \pi$
replacing $\theta$ by $4 x$ means that $4 x$ must have the same period
and therefore each $x$ of the $4 x$ can only take up $\frac{2 \pi}{4} = \frac{\pi}{2}$ period length.

$\sin \left(\theta\right)$ has an amplitude of $\left[- 1 , + 1\right]$
$\rightarrow$ for any angle $4 x$, $\sin \left(4 x\right)$ must be a value $s \epsilon \left[- 1 , + 1\right]$
and
$\rightarrow 2 \sin \left(4 x\right)$ must be $2 s$ giving it a range of $\left[- 2 , + 2\right]$