Sections:

Transformations of Trigonometric Functions, Page 16

Amplitude, Period, and Phase Shift (continued)

Example 2:

Graph f(x) = -1/3 sin(3x + pi/4). What is the amplitude, period, and phase shift of this function? 

Amplitude equals 1/3; Period equals 2pi over k equals 2pi/3

Phase Shift c over k=-pi/4 divided by 3 equals -pi/12 , c < 0 so the graph shifts to the left.

Now graph this function one step at a time.

First, graph f(x) = 1/3 sin(x):
 
graph of f(x) = 1/3 sin(x)

Next, graph f(x) = -1/3 sin(x):
 
graph of f(x) = -1/3 sin(x)

Next, graph f(x) = -1/3 sin(3x): 

graph of f(x) = -1/3 sin(3x)

Finally, you can graph f(x) = -1/3 sin(3x + pi/4):
 
graph of f(x) = -1/3 sin(3x + pi/4)