Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Understand and use the amplitude and period of a trigonometric function and the relationships between graphs of related trigonometric functions
Learning Objective/s:
  • Describe how amplitude, period, phase shift and vertical shift affect the graph of sinusoidal functions.
  • Calculate amplitude, period, phase shift and vertical shift from a given trigonometric equation.
  • Sketch transformed sine, cosine and tangent graphs using a systematic step‑by‑step procedure.
  • Explain the relationships between the graphs of sin, cos, tan and their reciprocal functions.
Materials Needed:
  • Projector or interactive whiteboard
  • Graphing calculator or Desmos access
  • Worksheet with practice problems
  • Printed sinusoid transformation cards
  • Rulers and coloured pencils for sketching
  • Teacher’s note cards with key formulas
 Introduction:
Begin with a quick visual of a simple sine wave projected on screen, asking students what features they notice. Recall previous work on basic sine and cosine graphs and the concept of period 2π. Explain that today they will learn how amplitude, period, phase and vertical shifts reshape these graphs and how related functions are linked. Success will be measured by correctly sketching a transformed sinusoid and identifying its parameters.
Lesson Structure:
  1. Do‑Now (5'): Short quiz on standard periods of sin, cos, tan.
  2. Mini‑lecture (10'): Review the general form y = a sin(bx + c) + d and define each parameter, showing formulas for amplitude and period.
  3. Guided demonstration (12'): Teacher models step‑by‑step sketch of y = 3 sin(2x – π/4) + 1, highlighting each transformation.
  4. Paired practice (15'): Students calculate parameters and sketch graphs for worksheet problems 1‑3; teacher circulates to check understanding.
  5. Relationship exploration (8'): Pairs match sin, cos, tan graphs using phase‑shift and reciprocal relationships.
  6. Check for understanding (5'): Exit ticket – write the amplitude, period and phase shift for a given equation.
Conclusion:
Summarise the key steps: set the mid‑line, plot amplitude, determine period, apply phase shift, then draw the curve. Students submit their exit tickets, reinforcing parameter identification. Assign homework: complete the remaining practice questions and sketch a transformed secant graph. Remind them to use the checklist when preparing for the upcoming test.