Lesson 3: The Unit Circle
Focus
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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?
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