Table

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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

Table 7: Library of Polar Equations

Table 7: TABLE 7

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