Course: Trigonometry
Topic: Trigonometric Identities
Subtopic: Half-Angle Identities


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).


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


Terms you should be able to 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.

Mini-Lectures and Examples

STUDY: Trigonometric Identities - Double-Angle IDs & Half-Angle IDs

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

rev. 2020-10-19