1. Lesson 3

Mathematics 30-1 Module 5

Module 5: Trigonometry Applications and Identities

 

Lesson 3: Trigonometric Identities

 
Focus

 

This picture shows two cars. One is a red and white race car the other is a green and black race car.

red car: iStockphoto/Thinkstock; green car: iStockphoto/Thinkstock



Success in Formula 1 racing requires a powerful, lightweight, high-performance engine that is durable. For maximum speed and fuel efficiency, an aerodynamic design is used. The cockpit, also called the survival cell, is created out of carbon fibre and is designed with multiple safety features.

 

Suppose you own two race cars that are identical except for the colour. Would you expect the two cars to perform the same? Does it matter which car you race with? Is it reasonable to switch one car for the other and expect a similar result?

 

In this lesson you will learn about mathematical identities, which include expressions that look different but generally act the same.

 

Lesson Outcomes

 

At the end of this lesson you will be able to

  • verify a trigonometric identity graphically and numerically
  • determine non-permissible values for a trigonometric identity
  • use the reciprocal, quotient, and Pythagorean identities to simplify an expression
  • explain the difference between an identity and an equation
Lesson Questions

 

In this lesson you will investigate the following questions:

  • How can you determine whether or not an expression is a trigonometric identity?
  • How can trigonometric identities be used to simplify problems?
Assessment

 

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

  • completion of the Lesson 3 Assignment (Download the Lesson 3 Assignment and save it in your course folder now.)
  • course folder submissions from Try This and Share activities
  • additions to Glossary Terms and Formula Sheet