Sections:

Transformations of Trigonometric Functions, Page 15

Amplitude, Period, and Phase Shift

Pen drawing a graph

Work through the following examples to see how you can put the amplitude, period, and phase shift together on one graph.

Example 1:

Graph f(x) = 2cos(2x - pi). What is the amplitude, period, and phase shift of this function? 

Amplitude equals 2; Period equals 2pi over k equals 2pi over 2 equals pi

Phase Shift = c over k equals pi over two, c > 0 so the graph shifts to the right. 

To look closely at how this is graphed, break down this function’s equation, step by step.

First, graph f(x) = 2cos(x): 

graph of f(x) = 2 cos(x)

Next, graph f(x) = 2cos(2x):

graph of f(x) = 2 cos(2x)

Now you can graph f(x) = 2cos(2x - Pi):

graph of f(x) = 2cos(2x - pi)