Polar Equation Graphs

5 major kinds of Polar Graphs

• Circles r = a sin • Lamicons r = a + b sin • Roses r = a sin (n• Archimedean Spiral r = a ± bθ• Lemniscates r2 = a2 sin 2

Circles

• General Form

• r = a cos θ• r = a sin θ

Lamicons

r = a ± b cos θ or r = a ± b sin θ

3 scenariosa = b cardioids

a > b dimpled

a < b loopy

Cardioids (Lamicon)a = b

• General form r = a ± a cos θ or r = a ± a sin θ

Basically a vaguelyHeart shaped graph

Can be an upside down or sideways heart.

Always includes the origin

Lamiconsa > b

Does not everInclude the origin

Lamiconsa < b

Includes an Inner loop

Always includes The origin

Roses

r = a cos bθa determines radius b relates to the petals

r = 3 cos 2θ

Archimedian Spiral

r = a ± bθ