Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Trigonometry: trig functions, identities, equations, solutions, graphs
Learning Objective/s:
  • Describe the six fundamental trigonometric functions and their unit‑circle definitions.
  • Apply Pythagorean, reciprocal, quotient, sum/difference, double‑angle and half‑angle identities to simplify expressions.
  • Solve basic trigonometric equations and write general solutions using periodicity.
  • Sketch the graphs of sine, cosine and tangent (including transformations) identifying period, amplitude, phase shift and asymptotes.
Materials Needed:
  • Projector or interactive whiteboard with slides on trig identities.
  • Textbook or handout containing tables of exact values and identity sheets.
  • Graph paper and coloured pencils for sketching functions.
  • Scientific calculators (or graphing calculator app).
  • Worksheet with practice equations and graph‑transformation tasks.
  • Whiteboard markers and eraser.
 Introduction:
Begin with a quick visual of a unit circle to remind students of the six trig functions. Review the exact values for the common angles that were covered last lesson. Explain that today’s success criteria are to correctly use identities, solve equations and accurately sketch transformed graphs.
Lesson Structure:
  1. Do‑Now (5’) – Short quiz on exact values and basic definitions displayed on the board.
  2. Mini‑lecture (15’) – Review the six functions and present key identities (Pythagorean, reciprocal, quotient, co‑function, even‑odd) with examples.
  3. Guided practice (10’) – Work through sum/difference and double‑angle formulas together using the projector.
  4. Equation‑solving activity (15’) – In pairs, solve a set of trigonometric equations and share general solutions.
  5. Graphing workshop (15’) – Students sketch sine, cosine and tangent graphs, then apply a transformation (e.g., y = 2 sin(3x − π/4)+1) identifying amplitude, period, phase shift and vertical shift.
  6. Check for understanding (5’) – Exit ticket: one problem requiring an identity or graph characteristic.
Conclusion:
Summarise how the identities simplify both algebraic manipulation and graph interpretation. Collect exit tickets to gauge understanding and assign a worksheet for homework that reinforces solving equations and graph transformations. Remind students to memorise exact values and practice sketching with different amplitudes and periods.