Name	Cardioid	Limaçon without inner loop	Limaçon with inner loop
Polar equations	\(r=a\pm a \ \cos\theta,\;a>0\)	\(r=a\pm b \ \cos\theta,\;0\lt b\lt a\)	\(r=a\pm b \ \cos\theta,\;0\lt a\lt b\)
	\(r=a\pm a \ \sin\theta,\;a>0\)	\(r=a\pm b \ \sin\theta,\;0\lt b\lt a\)	\(r=a\pm b \ \sin\theta,\;0\lt a\lt b\)
Typical graph

Name	Lemniscate (See p. 677)	Rose with three petals	Rose with four petals
Polar equations	\(r^2 = a^2 \ \cos (2\theta),\;a>0\)	\(r=a \ \sin(3\theta),\;a>0\)	\(r=a \ \sin(2\theta),\;a>0\)
	\(r^2 = a^2 \ \sin (2\theta),\;a>0\)	\(r=a \ \cos(3\theta),\;a>0\)	\(r=a \ \cos(2\theta),\;a>0\)
Typical graph