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

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

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.