Brought to you by Tutorial Services – The Math Center Trigonometric Identities Brought to you by Tutorial Services – The Math Center

In this workshop we will: Look at basic Identities. How other identities can be derived from basic identities. Look at Sum and Difference Identities. Look at Double-Angle and Half-Angle Identities. Look at Product and Sum Identities. How to develop a strategy for solving trigonometric identities.

Identities from the Definitions Basic Identities Every trigonometric function is related to the other because they are all defined in terms of the coordinates on a unit circle. Identities from the Definitions

Reciprocal Identities Basic Identities From the basic Identities we can define the Reciprocal Identities Reciprocal Identities

Pythagorean Identities Basic Identities The Pythagorean Identities can be derived from the fundamental identity Pythagorean Identities

Sum and Difference Identities These identities are used in solving equations and in simplifying expressions. Sum or Difference (Sines, Cosines)

Sum and Difference Identities These identities are used in solving equations and in simplifying expressions. Sum or Difference (Tangents)

Double-Angle and Half-Angle Identities The double-angle and half-angle identities are special cases of those identities. Double-Angle Identities

Double-Angle and Half-Angle Identities The double-angle and half-angle identities are special cases of those identities. Half-Angle Identities

Product and Sum Identities These identities are used to solve certain problems, but not used as often. Product-to-Sum Identities

Product and Sum Identities These identities are used to solve certain problems, but not used as often. Sum-to-Product Identities

Developing Strategy Verifying identities takes practice! The goal is to prove that both sides are equal to one another. You may work with one or both sides of the equation. Rewrite the expressions in terms of sines and cosines only. Other algebraic methods can be used such as factoring, finding the LCD or cross-multiplying. Verify that the following is an identity:

This is now verified by the Pythagorean Identity Developing Strategy Solution: This is now verified by the Pythagorean Identity

Developing Strategy Now try some on your own. Verify that the following is an identity: Tip: Basic cross-multiplication can simplify your verification!

Verify that the following is an identity: Developing Strategy Verify that the following is an identity: Tip: Stick to sines and cosines and work with both sides of the equation. Don’t forget your rules for basic math!

Trigonometric Identities Links Trigonometric Identities Handout Trigonometric Formulas Handout Equation of a Circle Handout Trigonometric Substitution Quiz Trigonometric Identities Quiz