polars

sine odd rose curve

one petal y-axis in the opposite direction of the sign of a

sine even rose curve

no petal will graph on the y-axis

cosine odd rose curve

one petal will graph on the x-axis in the direction of the sign of a

cosine even rose curve

petals will graph on both the x-axis and y-axis

sine limacon

will graph on y-axis

a = postive sine limacon

graph on postive y-axis

a = negative sine lima con

will graph on negative y-axis

cosine lima con

will graph on x-axis

a = postive cosine lima con

will graph on postive x-axis

a = negative cosine lima con

will graph on negative x-axis

sine circle (r = a* sin *theta)

will graph on y-axis

sin circle if a> 0

will graph on postive y-axis

sin circle if a<0

will graph on negative y-axis

cosine circle

will graph on x-axis

cosine circle a>0

circle is on postive a-axis

cosine circle a<0

negative x-axis

if r=a

circle will be centered at the pole with a radius of the absolute value of a

if 1 < a/b < 2

dimpled lima con

a/b = 1

cardoid

a/b < 1

lima con with an inner loop