Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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:

• 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

Terms you should be able to define: identity, trigonometric identity, mathematical proof

Memorize! these FUNDAMENTAL/BASIC IDENTITES

Mini-Lectures and Examples

Supplementary Resources (optional)

rev. 2020-10-19