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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Trigonometry
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:

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