Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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:

• 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

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