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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