Polar Graphs

Test for symmetry and polar graph types

replace (r, theta) by (r,-theta) or (-r, pi-theta)

test for symmetry about the x-axis

replace (r, theta) by (-r, -theta) or (r, pi-theta)

test for symmetry about the y-axis

replace (r, theta) by (-r, theta) or (r, pi+theta)

test for symmetry about the origin

Limacon with inner loop

r= a+b sin theta / r= a+b cos theta, a/b < 1

Limacon family- cardiod

r= a+b sin theta / r= a+b cos theta, a/b = 1

Dimpled limacon

r= a+b sin theta / r= a+b cos theta, 1 < a/b < 2

Convex limacon

r= a+b sin theta / r= a+b cos theta, a/b __>__ 2

Circle

r= _ sin theta / r= _ cos theta

Rose family

r= b sin (nTheta) / r= b cos (nTheta)

Affects the radius of each petal

How does *b* affect the graph?

Affects the # of petals

even= # of petals double

odd- same # of petals

How does *n* affect the graph?

Lemniscate family

r^2= a^2 sin (2 theta) / r^2= a^2 cos (2 theta)

Archimedes’ spiral

r= theta