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Course: Trigonometry
Topic: The Six Trigonometric Functions
Subtopic: Basic Identities

Overview

Now that we have defined the six trig functions, we can begin to find relationships between them. These relationships are called identities. We will use these identities to simplify trigonometric expressions and to create even more identities. Simplifying a trig expression can be accomplished in many ways but the goal is to get it as simplified as possible.

The major techniques used to simplify a trig expression are:

• Convert to sines and cosines
• Use LCDs to combine fractions
• Rewrite expressions by substituting with known identities
• Perform an algebraic manipulations such as distributive law, FOIL, factor, simplify compound fractions

Objectives

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

• 1.3.1 Use proper mathematical notation to write trig functions.
• 1.3.2 Given a trig ratio, information about the quadrant in which the angle lies, be able to sketch the triangle, label it properly, and find another trig ratio. For example, given tanθ=7/24, cosθ<0, find secθ.
• 1.3.3 Use the reciprocal identities, ratio identities, and Pythagorean identities to simplify trigonometric expressions.

Terminology

Memorize the 3 reciprocal identities, the 2 ratio identities, and the 3 Pythagorean identities. These are too important and used too often to just have on paper. Commit them to your memory!

Supplemental Resources (optional)

Videos from James Sousa's MathIsPower4U:
Mini-Lesson: Trig Identities:  Reciprocal, Quotient, Pythagorean
Mini-Lesson: Fundamental Identities:  Reciprocal, Quotient, Pythagorean