Lesson Plan

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Lesson Plan
Grade: Date: 18/01/2026
Subject: Mathematics
Lesson Topic: Trigonometry: further identities, equations, solutions
Learning Objective/s:
  • Apply key trigonometric identities (reciprocal, Pythagorean, sum‑to‑product, multiple‑angle) to simplify expressions.
  • Solve trigonometric equations by rewriting, isolating, and finding principal and general solutions.
  • Check solutions for extraneous values and verify using the unit circle.
  • Use appropriate identities to solve equations involving double, triple, and sum‑to‑product forms.
  • Communicate solution steps clearly in written form.
Materials Needed:
  • Projector or interactive whiteboard
  • Student worksheets with practice equations
  • Scientific calculators
  • Unit‑circle diagram handout
  • Whiteboard markers and erasers
 Introduction:
Begin with a quick recall of the basic sine, cosine and tangent identities, then pose a puzzling equation on the board to spark curiosity. Remind students they have previously mastered single‑angle identities and will now extend this knowledge to more complex forms. Explain that by the end of the lesson they will be able to manipulate and solve trigonometric equations confidently and justify each step.
Lesson Structure:
  1. Do‑now (5') – Short quiz on reciprocal and Pythagorean identities.
  2. Mini‑lecture (10') – Review sum‑to‑product, product‑to‑sum, double‑ and triple‑angle identities with projected examples.
  3. Guided practice (15') – Work through Example 1 as a class, modelling each solution step.
  4. Collaborative activity (15') – Pairs solve Example 2 and Example 3 on worksheets; teacher circulates to question.
  5. Whole‑class discussion (10') – Groups share solutions, highlight common pitfalls, and refine general‑solution writing.
  6. Exit ticket (5') – Students write a new trigonometric equation and outline the steps they would use to solve it.
Conclusion:
Summarise the systematic approach: simplify with identities, isolate the function, find principal angles, then extend to the general solution while checking for extraneous results. The exit ticket provides a quick retrieval check of the strategy. For homework, assign a set of three varied trigonometric equations for students to solve using today’s methods.