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A circle in parametric form

A circle centred at the origin can be written with the cosine and the sine of the same parameter. The radius is the factor in front of both, and the parameter is the angle. Then $x^2 + y^2$ equals the radius squared, because $\cos^2 t + \sin^2 t = 1$. If you want the centre somewhere else, you add the centre coordinates. One full turn corresponds to the parameter increasing by $2\pi$.

Symbols

Example

$[3\cos t, 3\sin t]$ has radius $3$. For $t = 0$ the point has $x = 3$ and $y = 0$, and $3^2 + 0^2 = 9$.

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Part of Mathematics R1: Parametric curves.