# X-Coordinate of the involute of a circle

## Description

An involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. It is a roulette wherein the rolling curve is a straight line containing the generating point. The involute of a circle resembles, but is not, an Archimedean spiral.

Its successive turns are parallel curves with constant separation distance, a property which is often (inaccurately) ascribed to the Archimedean spiral.

## Variables

x | X-coordinate of the point (dimensionless) |

a | Radius of the circle (dimensionless) |

t | Angle parameter in radians (dimensionless) |