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.