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:
- 5.4.1 Use half-angle formulae to evaluate trig functions
- 5.4.2 Use half-angle formulae to prove other trig identities
- 5.4.3 Solve problems involving a half-angle
Terminology
Define: half-angle
Supplementary Resources
You may want to download/print a copy of my Trigonometric Identities and Formulas Sheet to use as a reference. I included the product formulas and factoring formulas although they are not very useful in trig, they are used in calculus. Other good formula sheets you might want to use for reference include Trigonometry Review Sheet from Cengage or Trigonometry Cheat Sheet from Paul's Notesbut remember you are absolutely REQUIRED by the Clark College Mathematics Division to memorize the unit circle and not rely on a cheat sheet.