For the cardioid given parametrically as
| 
 
(1)
 
 | |||
| 
 
(2)
 
 | 
the involute is given by
| 
 
(3)
 
 | |||
| 
 
(4)
 
 | 
which is a mirror-image cardioid with .
For the cardioid given parametrically as
| 
 
(1)
 
 | |||
| 
 
(2)
 
 | 
the involute is given by
| 
 
(3)
 
 | |||
| 
 
(4)
 
 | 
which is a mirror-image cardioid with .
Weisstein, Eric W. "Cardioid Involute." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CardioidInvolute.html