Find the period range and amplitude of the cosine function y = -3cos4x

Solution:

The graphs of the cosine function y = cos x and y = -3cos4x has been plotted on the graph:

The period range of y = 3cos4x is one-fourth of the period range of y = cosx.

In other words, the number of cycles of y = 3cos4x in the same time period is 4 times that of y = cosx.

The amplitude is three times that of y = cosx as evident from the graph.

Find the period range and amplitude of the cosine function y = -3cos4x

Summary:

The period range of y = -3cos4x is π/2. The amplitude is 3.