The pedal curve of an epicycloid
(1)
 
(2)

with pedal point at the origin is
(3)
 
(4)

For an cusped epicycloid with , the pedal curve with pedal point at the origin is
(5)
 
(6)

Noting that
(7)
 
(8)

so solving for gives
(9)

and plugging in gives a polar equation of
(10)

which is the equation of a rose curve (Lawrence 1972, p. 204).