Pythagorean Identity
This figure illustrates the Pythagorean Identity which relates the squares of sine and cosine to the length of one on the unit circle.
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The pythagorean identity relates the sides of the right triangle together using only the angle of the right triangle. The identity is derived using pythagorean's theorem and the properties of the unit circle.
The unit circle is a circle of radius one placed at the origin of the coordinate system. This article discusses how the unit circle represents the output of the trigonometric functions for all real numbers.