Unit Circle Lesson Plan

Instructor: Dana Dance-Schissel

Dana teaches social sciences at the college level and English and psychology at the high school level. She has master's degrees in applied, clinical and community psychology.

Do you feel like you're circling the drain with your instruction on unit circles? helps you simplify your instruction with a video lesson featuring built-in problems to challenge and instruct your students. A simple in-class activity solidifies understanding. To keep the instruction moving forward, why not try our suggestions for related lessons and supplementary activities?

Learning Objectives:

Upon completion of this lesson, students will be able to:

  • explain what a unit circle is
  • use a unit circle to understand angles


30 minutes to 1 hour

Curriculum Standards


Prove that all circles are similar.


Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Key Vocabulary

  • Cosine
  • Sine


  • Begin by asking students to define a unit circle. Have them share their definitions for class discussion.
  • Now show the video lesson Reference Angles & the Unit Circle, pausing at 1:59.
  • Were students correct in their definitions? Why or why not? Discuss briefly as a class.
  • Next have students draw a unit circle on their papers using the one displayed on the screen as a model. They must also mark all reference angles and equivalent angles in radians as instructed in the video lesson.
  • When all students have completed their sketch of the unit circle, resume the video lesson pausing again at 2:28.
  • Have the students attempt to find the answer to the problem displayed on the screen using their unit circles.
  • Play the video again, pausing this time at 2:55. How many students were able to find the correct answer? For those who did not, do they understand how to do so now?
  • Play the video again and pause at 3:00.
  • Ask the students to try to solve the problem displayed on the screen.
  • When all students have finished, play the video again and pause it at 3:21. How many students found the correct answer this time? For those who didn't, can they find it now using the video lesson's explanation?
  • Now play the remainder of the lesson for the class.
  • Finally, give the students a list of angles for which they must fine the cosines and sines using their unit circles.

Discussion Questions

  • How is a unit circle different from just any circle, or is it?
  • Why is it important to understand angles in the real world?


  • Have students create a larger and colorful model of a unit circle using a pair plate. This can be used for reference going forward.
  • Ask students to identify all of the circles in the classroom. Can they apply the same principles to these circles as they did their unit circles?

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