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: Sum/Difference Identities

Overview

Our current arsenal of identities include the reciprocal, ratio, and Pythagorean. In today's lesson we add to that the sum and difference identities which expand trig functions of a sum of angles or of a difference of angles such as cos(x+pi/3). These will be useful, among other things, to evaluate trig functions of non-"nice" angles (such as 15^o or pi/12 as opposed to the "nice" angles such as 45^o or pi/2).

Objectives

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

• 5.2.1 Use sum/difference formulae to evaluate trig functions
• 5.2.2 Use sum/difference formulae to prove other trig identities
• 5.2.3 Solve problems involving a sum or difference in the angle

Terminology

Terms you should be able to define: sum of angles, difference of angles

You do not need to memorize these SUM/DIFFERENCE IDENTITIES.
You do need to know how to apply them. Keep a copy handy. Mini-Lectures and Examples

Supplementary Resources (optional)

rev. 2020-10-19