1. Lesson 4

1.8. Explore 4

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

In Try This 3, you saw that it is possible to use a sinusoidal regression with a graphing calculator to quickly and fairly accurately find a curve of best fit for sinusoidal data. You may have also found that it is possible to determine points on the curve.

 

Consider the following. Suppose you have a regression equation of where x represents time and y represents height. If you want to determine the times when y = 4.5, it is possible to substitute y = 4.5 into the equation and solve as follows:

 

 

 

But this process is somewhat complicated. An easier strategy is to graph the equations and y = 4.5 and then find the x-value of the intersections.

 

This graph shows the functions y = 3.1 sin(0.5(x minus 7.6)) + 4.0 and y = 4.5 and their intersections of the two functions at (0.99,4.5), (7.92,4.5), (13.56, 4.5), (20.49, 4.5), and (26.13, 4.5).

 

From the intersections in the graph, you can see that possible x-values include 0.99, 7.92, 13.56, 20.49, and 26.13.



textbook

Read “Example 3” on page 539 of you textbook to see another example of solving for x using an intersection. This example also shows how you can check your solutions.

 

 

Self-Check 2

 

Complete questions 3, 6, and 9 on pages 542 to 545 of your textbook. Answers


glossary

Add regression to your copy of Glossary Terms.