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

2. 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.

3. 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

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

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

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

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

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

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

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

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

12. 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:

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

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

15. 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!

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