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.

Related formulas

Variables

xX-coordinate of the point (dimensionless)
aRadius of the circle (dimensionless)
tAngle parameter in radians (dimensionless)