Mathematics 30-1 Module 5

These are two combined graphics. On the left is an illustration showing four pistons connected to a crankshaft. On the right is a photo of a race car travelling quickly down the racetrack.

pistons: © Alexandr Mitiuc/27283166/Fotolia; car: © Sly/388936/Fotolia

Racing a car includes many repetitive and some non-repetitive aspects to which trigonometry can be applied. In the first part of Module 5 you will explore how problems can be modelled and solved using sine, cosine, and tangent functions. In the second part you will begin to develop a set of tools that are useful in more advanced mathematics, and you will explore how you can determine whether these tools work properly.

These are two combined graphics. On the left is an illustration of a car tire, a brake, and a suspension. On the right is a photo of a drag-racing car.

tire: © nali/15258043/Fotolia; dragster: © Robert Young/2721726/Fotolia

In this module you will investigate the following questions:

How can trigonometry be used to model and solve problems involving motion?
What are the uses and limitations of a trigonometric identity?

To investigate the module questions, you will focus on the lessons and questions listed in the following table.

Lesson	Topic	Lesson Questions
1	The Tangent Function	How can the tangent function be represented graphically?
1	The Tangent Function	How can the tangent function be used to solve problems?
2	Equations and Graphs of Trigonometric Functions	How can a problem be solved using a trigonometric model?
3	Trigonometric Identities	How can you determine whether or not an expression is a trigonometric identity?
3	Trigonometric Identities	How can trigonometric identities be used to simplify problems?
4	Using Identities to Solve Equations	How can trigonometric identities be used to solve problems?
5	Proving Trigonometric Identities	How can a trigonometric identity be proven?
5	Proving Trigonometric Identities	Why is it necessary to prove an identity?

This photo is of a female race car driver.

The Module 5 Project: Pushing the Limits of Vehicle Performance will focus on how trigonometry can be used to determine various distances at a drag race and what speed and angle are required to allow a vehicle to jump over a large obstacle. You will complete the Module 5 Project as you work through the lessons.

Did You Know?

Female racers have become more common in recent years. A current star is Danica Patrick, a well-known racer who has competed in both the Formula 1 and NASCAR leagues with numerous top five finishes in each racing circuit. A highlight of her career was winning the Indy Japan 300 race.

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Module 5 Introduction