1. Lesson 3

Mathematics 30-1 Module 4

Module 4: Foundations of Trigonometry

 

Lesson 3: The Unit Circle

 
Focus

 

This is a photo of water ripples formed as circles coming from a central point.

Photos.com/Thinkstock

How many circles can you count in the water ripple shown in the photograph? The circles are different sizes. How can you describe their sizes?

 

So far in this module you have learned about radian angle measure and arc length. You used proportions to determine the radian measure of an angle when given the angle in degrees. You also learned how to determine the length of an arc on a circle.



Many trigonometric problems can be simplified by referencing a circle with a particular radius. What radius do you think would make both radians and arc lengths easiest to work with?

 

 
This sketch shows an angle in standard position with the terminal arm in the third quadrant. An unknown radius is labelled on the initial arm.

 

Lesson Outcomes

 

At the end of this lesson you will be able to

  • derive the equation of the unit circle
  • determine the coordinates of points of intersection of an angle’s terminal arm and the unit circle
  • generalize the equation of a circle with centre (0, 0) and radius r
Lesson Questions

 

You will investigate the following questions:

  • How is an equation of a unit circle derived?
  • How are points on the unit circle determined?
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
Materials and Equipment

 

You will need

  • paper
  • scissors
  • tape
  • can or other cylinder
  • straight edge