Lesson Plan

• Describe the definitions of the six trigonometric functions in a right‑angled triangle.
• Derive the quotient, reciprocal, Pythagorean, co‑function and even‑odd identities using standard algebraic steps.
• Apply these identities to construct clear, step‑by‑step proofs of given trigonometric statements.
• Solve moderate‑difficulty proof problems accurately and justify each transformation.

• Projector and screen
• Whiteboard and markers
• Printed handout of the identity summary table
• Worksheet with practice proof questions
• Scientific calculators
• Ruler and protractor for triangle sketches

Begin with a quick recall of how sine and cosine are defined from a right‑angled triangle, linking this to students’ prior work on basic trigonometric ratios. Explain that today’s focus is on proving the deeper relationships that connect all six functions. State the success criteria: students will be able to demonstrate each identity and use them in a proof.

1. Do‑Now (5 min): short quiz on the six function definitions.
2. Mini‑lecture (10 min): introduce quotient and reciprocal identities with quick examples.
3. Guided proof (15 min): derive the Pythagorean identities using the $a^{2}+b^{2}=c^{2}$ triangle.
4. Collaborative activity (10 min): groups explore co‑function and even‑odd identities on the unit circle, presenting their reasoning.
5. Independent practice (15 min): students work on the three proof questions from the notes, teacher circulates for support.
6. Exit ticket (5 min): each student writes one identity proof they found most challenging and how they resolved it.

Summarise how the six families of identities interrelate and why they are powerful tools for simplifying trigonometric expressions. Collect exit tickets to gauge understanding, and assign the remaining worksheet problems as homework for further practice.