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**

STUDY: Trigonometric Identities - Sum/Difference IDs

**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__

rev. 2020-10-19