Fundamental Trigonometric Identities

The Building Blocks of Trigonometry

"These identities form the foundation of trigonometry - relationships that remain true for all values of angles"
sinĀ²A + cosĀ²A = 1
The Pythagorean Identity - The most fundamental relationship
Welcome to the world of trigonometric identities! These powerful relationships are the backbone of all trigonometric calculations.
šŸ“ Pythagorean Identity

The most fundamental identity: sinĀ²A + cosĀ²A = 1. This comes directly from the Pythagorean theorem applied to the unit circle.

sinĀ²A + cosĀ²A = 1
True for any angle A
šŸ”— Tangent Identity

Derived from the Pythagorean identity by dividing through by cosĀ²A, giving us a relationship involving tangent and secant.

1 + tanĀ²A = secĀ²A
When cos A ā‰  0
šŸ”„ Cotangent Identity

Another derived identity obtained by dividing the Pythagorean identity by sinĀ²A, relating cotangent and cosecant.

cotĀ²A + 1 = cosecĀ²A
When sin A ā‰  0
āš” Applications

These identities are essential for simplifying expressions, proving other identities, and solving trigonometric equations.

Powerful Tools
From basic calculations to complex proofs

šŸŽ® Interactive Identity Explorer

Angle Controls:

30Ā°

Identity Verification:

sinĀ²A + cosĀ²A = 1.000
1 + tanĀ²A = 1.000
secĀ²A = 1.000
cotĀ²A + 1 = 1.000
cosecĀ²A = 1.000