# How do you graph  y=2cos5x?

Oct 28, 2016

Graph a cosine function with an amplitude of $2$ and a period of $\frac{2 \pi}{5}$.

#### Explanation:

Graph $y = 2 \cos 5 x$.

This equation is in the form $y = A \cos B x$ where

$A =$amplitude and $\frac{2 \pi}{B} =$ the period.

Amplitude is the distance on the y-axis between the center line of the graph and the "peak" or "trough".

Period is the distance on the x-axis of one full "cycle" or "repeat" of the graph.

Let's start with $y = \cos x$.. It has an amplitude of $1$ and a period of $2 \pi$.

Next, let's graph $y = 2 \cos x$. Notice the amplitude has doubled from $1$ on the red graph to $2$ on the blue graph.

Last, let's look at $y = 2 \cos 5 x$ in green. The period is $\frac{2 \pi}{5}$.
In other words, one complete "cycle" of cosine is graphed between zero and $\frac{2 \pi}{5}$.