Topic: Trigonometric Identities

Subtopic: Proving Trig Identities

**Overview**

A __trigonometric identity__ is a useful trigonometric formula that can be used to express a trigonometric expression in a different form. Some identities we have already covered include the reciprocal, ratio, and Pythagorean identities. Our goal over the next few days is to derive new trig identities, expand techniques for simplifying trig expressions, and produce mathematically accurate proofs of known trig identities. This material is algebraically intensive.

**Objectives**

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

- 5.1.1 Prove a trigonometric identity by a variety of methods including: algebraically simplifying each side, using known identities to rewrite trig expressions, turning all into sines and cosines and simplifying
- 5.1.2 Know what one cannot do when proving a trigonometric identity such as performing an operation or applying a function to both sides of the original statement to be proved
- 5.1.3 Determine if a trig statement is an identity by graphing

**Terminology**

Define: identity, trigonometric identity, mathematical proof

**Memorize! these FUNDAMENTAL/BASIC IDENTITES**

**Supplementary Resources (optional)**

Videos from James Sousa's MathIsPower4U:

Mini-Lessons:

__Fundamental Identities: Reciprocal, Quotient, Pythagorean__

__Negative Angle Identities__

__Determining an angle and other trig function values given a trig function value__

Examples:

__Example 1: Simplifying a Trigonometric Expression__

__Example 2: Simplifying a Trigonometric Expression__

__Example 3: Simplifying a Trigonometric Expression__

Mini-Lesson:

__Verifying Identities using Basic Identities__

Examples:

__Example 4: Simplifying a Trigonometric Expression__

__Example 5: Simplifying a Trigonometric Expression__