Math lesson plan · 12th grade (Year 13 in England) · 60 minutes
Trigonometric identities
Trigonometry
CCSS HSF.TF.C.8
Objective and success criteria
Students will: Trigonometric identities.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: The unit circle and radians
Leads to: Use sin²θ + cos²θ = 1 to find exact values
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (The unit circle and radians). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Convert 120° to radians (in terms of π). (2π/3 / π/3 / 3π/4 / π/6) → 2π/3Prompt: A half turn is π radians.
- Is cos 120° positive, zero or negative? (Positive / Zero / Negative) → NegativePrompt: On the unit circle, cos is the x-coordinate and sin is the y-coordinate.
- Convert 150° to radians (in terms of π). (5π/6 / π/6 / π/4 / 2π/3) → 5π/6Prompt: A half turn is π radians.
Hook · 6 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Trigonometric identities. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: θ is acute and sin θ = 7/25. Find cos θ.
- Step 1: cos²θ = 1 − (7/25)² = 576/625
- Step 2: cos θ = 24/25
- Answer: 24/25
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- θ is acute and cos θ = 24/25. Find sin θ. → 7/25Prompt: Use sin²θ + cos²θ = 1.
- True for all angles θ? cos(−θ) = −cos θ (True / False) → FalsePrompt: Test it with a value, such as θ = 30°.
You do: independent practice · 17 min
- 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.
Exit ticket · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- θ is acute and sin θ = 5/13. Find cos θ. → 12/13Prompt: Use sin²θ + cos²θ = 1.
- True for all angles θ? sin²θ + cos²θ = 1 (True / False) → TruePrompt: Test it with a value, such as θ = 30°.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: The unit circle and radians.
- Use concrete materials: scientific calculators.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Use sin²θ + cos²θ = 1 to find exact values.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-12.
Free lesson plan from eurekami.com/lesson-plan-builder