Trigonometric Identities Lesson Plan

Instructor: Joanne Abramson

Joanne has taught middle school and high school science for more than ten years and has a master's degree in education.

Recognizing and utilizing trigonometric identities is an essential part of any pre-calculus curriculum. This lesson plan introduces the concept of trigonometric identities using videos, graphing calculators and the magic hexagon.

Lesson Objectives:

By the end of this lesson, students will be able to

  • Define the term 'trigonometric identity'
  • Name some of the most common categories of trigonometric identities
  • Use graphs to prove that a trigonometric equation is an identity


1-1.5 hours

Curriculum Standards:


Prove the Pythagorean identity sin^2(x) = cos^2(x) = 1 and use it to find sin(x), cos(x), or tan(x) given sin(x), cos(x), or tan(x) and the quadrant of the angle.


Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


  • 'Magic hexagon' worksheet
    • Create a hexagon divided into 6 equal triangles
    • Label the center '1.'
    • Label the vertices 'A'-'F,' starting with the top right and continuing clockwise.
  • Graphing calculators or graphing smart phone apps

Instructions - Part I

  • To begin the lesson, show the students a quote about identity (such as, ''Unless we base our identity on the truth of who we are, it is impossible to obtain true happiness,'' by Brenda Shoshanna.)
  • Ask students to define the term 'identity.' Lead the class to words such as 'true,' 'self' or 'identical.'
  • Explain that they will now be learning about a specific type of identity, a trigonometric identity.
  • Show the video Trigonometric Identities: Definitions & Uses. Pause at 1:05.
  • Ask students the following questions:
    • What were the two mathematical identities provided in the video?
    • What are some examples of other mathematical identities?
    • How many groups of identities are there in trigonometry?
  • Continue with the video. Pause at 2:27.
  • Ask students to name the seven different categories of trig functions. Write them on the board as they are called out. Continue until all seven groups are on the board. Show this section of the video again if necessary.
  • Return to the video, this time pausing at 3:15.
  • Ask students to provide examples of ways that they will use these identities in your class.
  • Watch the video to the end.
  • To check for understanding, project the lesson quiz and complete it as a class.

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