Lesson 3

In Lesson 2 you graphed both y = sin x and y = cos x and saw that they were very similar functions. Just as parameters can be used to interpret a sine function, the parameters a, b, c, and d correspond to characteristics for a function of the form y = a cos b(x − c) + d. Try This 2 explores how these parameters change the graph of the function.

Try This 2

1. Predict how the parameters a, b, c, and d will correspond to characteristics of the function y = a cos b(x − c) + d by completing a table similar to the following.
   
   

   	Description of Predicted Change
   Increase a
   Decrease a
   Increase b
   Decrease b
   Increase c
   Decrease c
   Increase d
   Decrease d

2. Following similar instructions as in Discover, open Cosine a, b, c, d Explorer and use this applet to check your predictions from question 1.
   
   
    
   

Save your responses in your course folder.

Share 2

With a partner or in a group, describe how changing the parameters a, b, c, and d are similar for the function y = a cos b(x − c) + d and the function y = a sin b(x − c) + d.

If required, save a record of your discussion in your course folder.