# How do you find the period and amplitude for y=1/4 cos((2x)/3)?

Jun 28, 2016

I found:
$\text{Amplitude} = \frac{1}{4}$
$\text{period} = 3 \pi$

#### Explanation:

The amplitude will be the number in front of your $\cos$, i.e., $\frac{1}{4}$; this tells you that your function oscillate between $\frac{1}{4}$ and $- \frac{1}{4}$.
The period is a bit more tricky; you use the number in front of the $x$ of the argument of $\cos$, i.e., $\frac{2}{3}$; let us call it $n$, so we have:
$\text{period} = \frac{2 \pi}{n} = \frac{2 \pi}{\frac{2}{3}} = 3 \pi$ this means that your function makes a complete oscillation in $3 \pi$ radians.

Graphically:
graph{(1/4)cos(2x/3) [-10, 10, -5, 5]}