Lesson: Double-Angle and Half-Angle Identities Mathematics

In this lesson, we will learn how to use the Pythagorean identity and double-angle formulas to evaluate trigonometric values.

Lesson Plan

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:
    • sinsincos2π‘₯=2π‘₯π‘₯
    • coscossincossin2π‘₯=π‘₯βˆ’π‘₯=2π‘₯βˆ’1=1βˆ’2π‘₯
    • tantantan2π‘₯=2π‘₯1βˆ’π‘₯
    • sincosπœƒ2=Β±ο„ž1βˆ’πœƒ2
    • coscosπœƒ2=Β±ο„ž1+πœƒ2
    • tansincoscossinπœƒ2=πœƒ1+πœƒ=1βˆ’πœƒπœƒ
  • 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.

Lesson Video

Video Thumbnail
15:41

Lesson Explainer

Sample Question Videos

  • 02:16
  • 01:47
  • 02:43

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