# How do you find the period, amplitude and sketch y=cos2pix?

Jan 8, 2018

In $y = a \cos \left(b \left(x - c\right)\right) + d$:

$a$ is the amplitude
$\frac{2 \pi}{b}$ is the period
$c$ is the phase shift, or horizontal transformation
$d$ is the vertical transformation

Here, the amplitude is $1$. The period will be $\frac{2 \pi}{2 \pi} = 1$.

At $x = 0$, $y = 1$ (a maximum) and at $x = \frac{1}{2}$, $y = - 1$ (a minimum).

Use this to get the following graph:

graph{y = cos(2pix) [-10, 10, -5, 5]}

Hopefully this helps!