Cal 3 Polar Coordinate Graphs

r=a

circle

r=a sin theta

circle above x-axis

r= a cos theta

circle to the right of the y axis

r= a theta

spiral

r= a+/- b sin theta

r = a +/- b cos theta

limacon

r= a+/- b sin theta

r = a +/- b cos theta

a

limacon with inner loop

r= a+/- b sin theta

r = a +/- b cos theta

a=b

cardiod

r= a+/- b sin theta

r = a +/- b cos theta

a>b

dimpled limacon

a >/= 2b

convex limavon

r= a sin n theta

r = a cos n theta

roses

r= a sin n theta

r = a cos n theta

r = a cos 2 theta

four-leaved rose

r= a sin n theta

r = a cos n theta

r = a cos 3 theta

three leaved rose

r= a sin n theta

r = a cos n theta

r = a cos 4 theta

eight leaved rose

r= a sin n theta

r = a cos n theta

r= a cos 5 theta

five leaved rose

r^2 = a^2 sin 2 theta

lemniscate not on the x axis (diagonal)

r^2 = a^2 cos 2 theta

lemniscate on the x axis