# How do you find the amplitude, period and graph #y=3cos(1/2theta)#?

##### 1 Answer

The amplitude is

#### Explanation:

This is a graph in the form

For a graph in this form, the amplitude is

To graph it, it is helpful to find certain easy-to-find points. Because

graph{cos(x) [-10, 10, -5, 5]}

Looking at the graph, the period is

graph{cos(.5x) [-10, 10, -5, 5]}

Currently the amplitude of the graph is

graph{3cos(.5x) [-10, 10, -5, 5]}

This process is equivalent to performing the appropriate transformations to the parent cosine graph: a vertical stretch by 3 and a horizontal stretch by 2.