Identity Basics and Trigonometric Function Identities

This section introduces fundamental concepts of trigonometric identities and their various types. The content explores how identities differ from regular equations and presents multiple categories of trigonometric identities.

Definition: An identity is a mathematical statement that remains true for any input variable, unlike equations which are only true for specific values.

Highlight: Rationalizing is considered an identity as it works consistently without variables.

The page covers several types of trigonometric identities:

Example: Quotient identities include tanθ = sinθ/cosθ and cotθ = cosθ/sinθ

Vocabulary: Pythagorean identities establish relationships between squared trigonometric functions, such as sin²θ + cos²θ = 1

The section also details verification methods for trigonometric identities:

1. Simplification of expressions through substitution
2. Equation verification by manipulating one side at a time

Highlight: When verifying identities, it's crucial not to square both sides or multiply by common denominators, as this can lead to incorrect results.