Lesson 4

1. Lesson 4

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

Lesson 4: Modelling Data with Sinusoidal Functions

Focus

This collage shows two photos. Left, this photo shows a showshoe hare in winter. Right, this photo shows a lynx hunting in winter.

left: Jupiterimages/Photos.com/Thinkstock, right: iStockphoto/Thinkstock

The Canadian lynx’s most important source of food is the snowshoe hare. When a predator has only a single significant source of food, the two populations follow a somewhat sinusoidal pattern as shown in the diagrams. Why does this cyclical pattern occur?

How reasonable is it to use a sinusoidal curve to model this data? Do you think this trend would continue for a long time?

The diagram shows the snowshoe hare and lynx populations for 15 years. Both populations fluctuate over a period of about 5 years. For each cycle, the peak of the lynx population occurs slightly after the peak of the hare population.

The diagram shows the oscillating behaviour of a predator and prey population. The peaks of the predator population occur shortly after the peaks of the prey population.

In this lesson you will explore various ways of using sinusoidal functions to represent data. You will then use these functions to help interpret the data.

Lesson Outcomes

At the end of this lesson you will be able to

determine a sinusoidal curve that best represents a set of data
interpret data using a sinusoidal curve of best fit

Lesson Question

You will investigate the following question: How can sinusoidal data be represented using a sinusoidal function?

Assessment

Your assessment may be based on a combination of the following tasks:

completion of the Lesson 4 Assignment (Download the Lesson 4 Assignment and save it in your course folder now.)
course folder submissions from Try This and Share activities
additions to Glossary Terms
work under Project Connection

Materials and Equipment

graphing software or graphing calculator