• Quick retrieval from earlier learning (The unit circle and radians; Exact trig values (0°, 30°, 45°, 60°, 90°)). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Convert π/4 radians to degrees. → 45Prompt: π radians is a half turn.
2. What is the exact value of sin 45°? (0 / 1 / √2/2 / 1/2) → √2/2Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
3. Is sin 90° positive, zero or negative? (Positive / Zero / Negative) → PositivePrompt: On the unit circle, cos is the x-coordinate and sin is the y-coordinate.

• Show a ramp or a ladder against a wall and ask how steep it is.
• Share the objective: Read exact coordinates on the unit circle. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: What are the coordinates of the point on the unit circle at an angle of 225°?
• Step 1: (cos 225°, sin 225°) = (−√2/2, −√2/2)
• Answer: (−√2/2, −√2/2)
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. What are the coordinates of the point on the unit circle at an angle of 225°? ((−√2/2, −√2/2) / (√2/2, −√2/2) / (−√2/2, √2/2)) → (−√2/2, −√2/2)Prompt: The point is (cos θ, sin θ).
2. Find the exact value of cos(7π/4). (−√2/2 / −√3/2 / √2/2 / √3/2) → √2/2Prompt: 7π/4 radians = 315°.

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. What are the coordinates of the point on the unit circle at an angle of 270°? ((−1, 0) / (0, −1) / (0, 1)) → (0, −1)Prompt: The point is (cos θ, sin θ).
2. Find the exact value of sin(7π/6). (√2/2 / 1/2 / −1/2 / −√2/2) → −1/2Prompt: 7π/6 radians = 210°.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.