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: 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+π/3). These will be useful, among other things, to evaluate trig functions of non-"nice" angles (such as 15° or π/12 as opposed to the "nice" angles such as 45° or π/2).

Objectives

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

Terminology

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.

Supplementary Resources (optional)

Mini-Lesson: Sum and Difference Identities for Cosine
Example: Using The Sum and Difference Identity to Determine a Cosine Function Value
Mini-Lessons:
Sum and Difference identities for Sine
Sum and Difference Identities for Tangent
Examples:
Simplify a Trig Expression Using the Sum and Difference Identities
Evaluate a Trig Expression Using the Sum and Difference Identities
Using The Sum and Difference Identity to Determine a Sine Function Value
Using The Sum and Difference Identity to Determine a Tangent Function Value