# How do you graph y = cos2x?

Jul 1, 2015

This is a cossine function that gives you a graph similar to the "normal" cosine with amplitude $1$ BUT period of $\pi$ only .

#### Explanation:

This is a cosine function with amplitude equal to $1$ (it comes from the one "in front" of $\cos$ that is not written but it is there!) and period obtained from the $2$ in front of $x$ in the argument as:
$p e r i o d = \frac{2 \pi}{\textcolor{red}{2}} = \pi$.

This value of the period tells you that this is not the normal cosine but it is "squeezed" to fit an entire oscillation between $0$ and $\pi$ instead of between $0$ and $2 \pi$ as the "normal" cosine.

Graphically:
$y = \cos \left(2 x\right)$
graph{cos(2x) [-10, 10, -5, 5]}

A "normal" cosine would look as:
$y = \cos \left(x\right)$
graph{cos(x) [-10, 10, -5, 5]}