Unit circle

File:Circle-trig6.svg
The Unit Circle can be used to model every Trigonometric function.

In mathematics, a unit circle is a circle with a radius of 1. The equation of the unit circle is <math>x^2 + y^2 = 1</math>. The unit circle is centered at the Origin, or coordinates (0,0). It is often used in Trigonometry.

Trigonometric functions in the unit circle

In a unit circle, where <math>t</math> is the angle desired, <math>x</math> and <math>y</math> can be defined as <math>\cos (t) = x</math> and <math>\sin (t) = y</math>. Using the function of the unit circle, <math>x^2 + y^2 = 1</math>, another equation for the unit circle is found, <math>\cos^2(t) + \sin^2(t) = 1</math>. When working with trigonometric functions, it is mainly useful to use angles with measures between 0 and <math>\pi\over 2</math> radians, or 0 through 90 degrees. It is possible to have higher angles than that, however. Using the unit circle, two identities can be found: <math>\cos (t) = \cos (2 \cdot \pi k + t)</math> and <math>sin (t) = \sin (2 \cdot \pi k + t)</math> for any integer <math>k</math>.

File:Unit circle.svg
The unit circle can substitute variables for trigonometric functions.