Lesson Plan: Double-Angle and Half-Angle Identities Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the Pythagorean identity and double-angle formulas to evaluate trigonometric values.

Objectives

Students will be able to

  • derive and recall the double- and half-angle identities for sine, cosine, and tangent from the sum and difference formulas:
    • sinsincos2𝑥=2𝑥𝑥
    • coscossincossin2𝑥=𝑥𝑥=2𝑥1=12𝑥
    • tantantan2𝑥=2𝑥1𝑥
    • sincos𝜃2=±1𝜃2
    • coscos𝜃2=±1+𝜃2
    • tansincoscossin𝜃2=𝜃1+𝜃=1𝜃𝜃
  • use the identities along with the Pythagorean identities to simplify expressions,
  • use the identities to evaluate expressions, including determining the exact values of trigonometric functions, for example, sin15.

Prerequisites

Students should already be familiar with

  • radians,
  • the Pythagorean identities,
  • the sum and difference formulas for sine, cosine, and tangent.

Exclusions

Students will not cover

  • solving equations.

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