# What is the amplitude of y=1/2costheta?

Jan 21, 2018

The 'peak to peak' amptitude of $y$ is $1$

#### Explanation:

$y = \frac{1}{2} \cos \theta$

Remember, $- 1 \le \cos \theta \le 1 \forall \theta \in \mathbb{R}$

Hence, $- \frac{1}{2} \le \frac{1}{2} \cos \theta \le \frac{1}{2}$

The 'peak to peak' amptitude of a periodic funtion measures the distance between the maximum and minimum values over a single period.

Hence, the 'peak to peak' amptitude of $y$ is $\frac{1}{2} - \left(- \frac{1}{2}\right) = 1$

We can see this from the graph of $y$ below.

graph{1/2cosx [-0.425, 6.5, -2.076, 1.386]}