The Fundamental Trigonometric Identities are formed from our knowledge of the Unit Circle, Reference Triangles, and Angles.
What’s an “identity” you may ask?
In mathematics, an “identity” is an equation which is always true, as nicely stated by Purple Math.
For example, 1 = 1, is an equation that is always true; therefore, we say it is an identity.
In previous math classes you learned some basic algebraic properties, such as the Distributive Property and the Associative Property, that enabled you to simplify algebraic expressions and solve equations.
Fundamental Pythagorean Identity
Well, in Trigonometry we have some basic properties that we refer to as Identities that enable us to evaluate other trigonometric functions, simplify and rewrite expressions, and eventually solve trigonometric equations.
In this lesson we will learn how to formulate and write the Fundamental Trig Identities:
- Basic Identities
- Reciprocal Identities
- Quotient (Ratio) Identities
- Pythagorean Identities
- Odd/Even (Negative Angle) Identities
From there, we will then discover how to use these Fundamental Identities to simplify or rewrite trigonometric expressions to get an equivalent expression or identity.
Trig Identities Cheat Sheet
- Trigonometric Identities Handout: This formula sheet contains Pythagorean Identities, Half and Double Angle Formulas, Sum and Difference Identities, Cofunctions, and more.
Basic Trig Identities – Video
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