A unit circle is any circle whose radius is $1$, and is used and a base simplification for any circle.
Using [[Coordinate System|coordinates]] of the [[Cartesion Plane]] whose origin is the center of this unit circle, the set of all points in that circle are equal to:
$\huge \begin{align}
C_{1} &= \setbuild{ (x,y) \in \R \times \R }{x^{2}+y^{2}=1}\\
\end{align}$
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