Module 4: Foundations of Trigonometry

 

In Try This 2 you investigated how to determine the equation of a graph that includes a phase shift and a vertical translation. There is only one possibility for d, and it is the value of the midline. However, c can have an infinite number of values and still result in the same graph. In the previous example, the possible values of c are π + 2nπ, n ∈ I. These values are true because if you translate the graph horizontally by a multiple of the period, the same graph results.

 

This diagram shows that translating horizontally by a multiple of the period results in the same graph.

 

You have seen how the parameters c and d affect the graph of a sine or cosine function. Next you’ll look at a few examples that use all four parameters a, b, c, and d.



textbook

Read “Example 4” on pages 244 to 246 of the textbook. This example shows how to determine an equation from a graph by finding a, b, c, and d.  You will notice that the same graph can be written in either standard form, or Note which parameters are the same between the two and which parameters are different.

 

Self-Check 2

 

Complete questions 6.a., 11.a., and 11.c. on pages 251 and 252 of the textbook. Answer