Reciprocal identities and quotient identities
, , ,  and .

Pythagorean identities:

, , and . 

Co-function identities:

,  and .

Sum and difference identities
,
and ; , and

 Double angle identities:

, and .

Power reducing and half angle formulas:

, and

,  and

Sum-to-product formulas:



 

Product-to sum formulas:

Flash Movie	Flash Game	Flash Card
Core Concept Tutorial	Problem Solving Drill	Review Cheat Sheet

This tutorial introduces the known trigonometric identities and how they are used to reduce trigonometric expressions. Known trigonometric identities are mentioned in this tutorial with the use of examples.

The fundamental trigonometric functions are shown in the examples provided with the use of relations and proportional identities. Two of the Pythagorean identities are derived with the knowledge of one of them.

Specific Tutorial Features:
• Examples using the fundamental identities and their application in the simplification trigonometric expression are discussed.
• Step by step examples are shown to present various trigonometric expressions and identities.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

Using and verifying identities
Fundamental trigonometric functions
Pythagorean identities
Simplifying expressions
Periodicity of trigonometric identities
Co-function identities
Difference identities
Sum identities
Double angle identities
Proof of double angle sine identities
Proof of double angle cosine identities
Negative angle formulas
Proof of sine negative angle formulas
Proof of cosine negative angle formulas
Power reducing formulas
Half angle identities
Sum-to-product formulas
Product-to-Sum formulas