# The unit circle definition of sine, cosine, and tangent

Contents
Learn how the trigonometric ratios are extended to all real numbers using algebra. Start solving simple problems that involve this new definition of the trigonometric functions.
Try some practice problems
Learn by doing or check your understanding

Learn about radians, which are the official unit of measurement for angles in algebra (in contrast to degrees, which are used in geometry).

### The unit circle definition of sine, cosine, and tangent

Learn about the ingenious way in which we define the trigonometric functions for any real number.

### The graphs of sine, cosine, and tangent

Learn how the graphs of y=sin(θ), y=cos(θ), and y=tan(θ) look, using the unit circle definition of the functions.

### Basic trigonometric identities

Learn about very useful trigonometric identities that arise by considering different properties of the unit circle definition.

### Trigonometric values of special angles

Learn how to find the trigonometric values of some special angles without the use of a calculator.

### The Pythagorean identity

Prove the Pythagorean trigonometric identity for all real numbers and use it in order to solve problems.

### Long live Tau

Watch videos by Sal and Vi that discuss the ongoing battle between the more popular Pi (π=3.14..) and its more qualified rival Tau (τ=6.28...).