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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

Define: identity, trigonometric identity, mathematical proof

Memorize! these FUNDAMENTAL/BASIC IDENTITES Supplementary Resources (optional)