How do you find the amplitude and period of #y = cos 4x#?

1 Answer
Aug 13, 2015

They can be determined by looking at the coefficients and their location.

Explanation:

Let's look at this equation:

#y = Acos(Bx)#

The #A# and #B# coefficients can tell us what the amplitude and period are.

First, #A# tells us what the amplitude is. For example, the amplitude of #y = 2cos(x)# would be simply #2#.

Second, #B# tells us what the period is. In this case, we have to divide the normal period by #B# in order to find the period.

For example, the period of cosine is #2pi#. Therefore, the period would be #[2pi]/B#

For your specific question, #y = cos4x#, the amplitude would be #1# and the period would be #[2pi]/4#, or #pi/2#.

NOTE: I wanted to mention to be careful when finding the period of tangent, as the normal period of tangent is #pi#. Therefore, to find the period, you would do #pi/B# instead.