Module 4: Foundations of Trigonometry

 

Lesson 7 Summary

 

Although sine and cosine functions can be transformed in the same manner as other functions, the characteristics of their graphs are given the more specific names of amplitude, period, phase shift and vertical displacement. These names correspond to the parameters of a, b, c, and d for a sine or cosine function written in the form or

 

Parameter Characteristic of Graph
a  a = amplitude
b
c c = phase shift right if c is positive, left if c is negative
d d = midline value

 

The amplitude, period, midline, and phase shift are labeled on this sinusoidal graph. The graph also shows that the amplitude equals a, the period equals 2 pi divided by b, the midline equals d, and the phase shift equals c.

 

In Module 5 you will begin to explore the graph of tangent functions and determine how to apply trigonometric functions to problems.