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A unit circle is a circle with a radius of one, typically centered at the origin of a coordinate system. It's a fundamental tool in mathematics, particularly in trigonometry, because it provides a simple way to define and visualize trigonometric functions and the relationships between angles and their corresponding values.
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Illustration of a unit circle. The variable t is an angle measure. Animation of the act of unrolling the circumference of a unit circle, a circle with radius of 1. Since C = 2πr, the circumference of a unit circle is 2π.
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S because it is a one-dimensional unit n-sphere.