Lesson Plan: Using the Addition Formula to Simplify 𝑎 cos 𝑥 ± 𝑏 sin 𝑥 Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the addition formula to simplify the expression 𝑎 cos 𝑥 ± 𝑏 sin 𝑥.


Students will be able to

  • simplify expressions of the form 𝑎𝑥±𝑏𝑥cossin to expressions involving the sine function or cosine function only,
  • sketch graphs of trigonometric functions of the form 𝑦=𝑎𝑥±𝑏𝑥cossin,
  • solve trigonometric equations by simplifying 𝑎𝑥±𝑏𝑥cossin.


Students should already be familiar with

  • radians and degrees,
  • angle sum and difference formulae,
  • double angle formulae,
  • sketching trigonometric graphs,
  • inverse trigonometric functions.


Students will not cover

  • simplifying trigonometric expressions that are not in the form 𝑎𝑥±𝑏𝑥cossin.

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