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Radians and the Unit Circle (Lesson 9.8)

Learning Targets
  • Find coterminal angles for angles measured in radians. 
  • Find reference angles on the unit circle in radians and degrees.
  • Evaluate trigonometric expressions using radian measures. 
Activity: Wheel of Algebra… Again!

Experience First

Before starting today’s lesson, have students fill in a blank unit circle with degrees and radians for a warm up. This page will be a reference tool for them as they work through today’s activity.


We’re revisiting the context from Lesson 9.5 with our prize wheel spinner. The activity is basically the same except for now we will do everything in radians. Each student will need a copy of the spinner again. Students can work through the whole activity in their groups. Have them write their answers on the board as they finish.

Guiding Questions

  • How many radians is each sector? How do you know?

  • If this question were being asked in degrees, what would you get? 

  • How many radians is one full spin around the circle?

  • How many radians is halfway around the circle?

  • How could you write 1π as a fraction that would be helpful? How could you write 2π as a fraction that would be helpful?

  • On your unit circle, where is the sine value equal to -½

Formalize Later

Our margin notes are pretty much the same as they were in Lesson 9.5 when we looked at the angles in degrees. As you debrief this with students, refer back to what they had learned before and tie it in to radians.


Consider having a practice day after this lesson, in which students find trig ratios for a variety of different angles (in both degrees and radians!).

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