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 their use in the simplification process of trigonometric expressions.  Known trigonometric identities helped reduce the time it takes to simplify trigonometric expressions.

The fundamental trigonometric functions are shown in the examples provided with relation to specific scenarios. The Pythagorean identities are derived with the knowledge of one of them. Difference and sum identities of the sine, cosine and tangent functions are shown in this tutorial. They come handy when simplification of trig expressions is needed.

Specific Tutorial Features:
• The various trigonometric formulas are shown in the examples.
• Step by step examples are shown to verify trigonometric 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