LESSON NOTES MENU
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Trigonometry
Topic: Trigonometric Identities
Subtopic: Half-Angle Identities

Overview

Continuing to expand our arsenal of useful trigonometric formulae, in today's lesson we study the half-angle identities which expand trig functions of a half-angle such as cos(x/2).

Caution: To avoid a common error, when determining the sign of the answer from a half-angle formula, remember that it is based on the quadrant of the half-angle, not the quadrant of the whole angle.

The half-angle identities are the last of the identities we study. In my opinion, you do not need to memorize all the trig identities we studied. However you MUST memorize the Pythagorean identities and the double-angle identities since they are used so frequently here and in calculus and engineering. The rest though can become a bit overwhelming. For them you may want to use a "cheat sheet" of identities (see below).

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: half-angle

You do not need to memorize these HALF ANGLE IDENTITIES.
You do need to know how to apply them. Keep a copy handy.

Supplementary Resources (required reading!)

This is also an appropriate time to start using a reference sheet of identities.

Supplementary Resources (optional)

Mini-Lesson: Half Angle Identities
Mini-Lesson: Verifying Identities:  Sum, Difference, Double, and Half Angle Identities
Example:  Rewrite a Trig Expression Using a Half Angle Identity
Example:  Determine a Cosine Function Value Using a Half Angle Identity
Example:  Determine a Sine Function Value Using a Half Angle Identity
Example:  Determine a Tangent Function Value Using a Half Angle Identity