Lesson 5: Trigonometric Equations

Focus

The Circuit Gilles Villeneuve is a motor-racing circuit in Montréal that hosts the Canadian Grand Prix car race. During this Formula 1 race, cars reach speeds of 360 km/h while traveling 70 laps around the 4.4-km loop.

Suppose you wanted to answer this question: How far has a car travelled when it crosses the finish line? You might answer 4.4 km, 8.8 km, or something else. How many answers are there? Is there a way to represent all of these answers without writing each one out?

In this lesson you will learn to solve some first- and second-degree trigonometric equations. You will also learn how to represent an infinite number of solutions as a general solution.

Lesson Outcomes

At the end of this lesson you will be able to

• determine the measure of angles that produce a given trigonometric ratio
• algebraically determine the solution to a first- and second-degree trigonometric equation over a restricted domain
• verify a solution to a trigonometric equation
• determine a general solution to a trigonometric equation
• solve problems using trigonometric ratios

Lesson Questions

You will investigate the following questions:

• How can trigonometric equations be solved?
• How is a specific solution for a trigonometric equation related to the general solution?

Assessment

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

• completion of the Lesson 5 Assignment (Download the Lesson 5 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