Alg 2/Precalc Honors- Special Polar Graphs

Convex Limacon

Convex Limacon

(a/b) ≥ 2

Cardioid

(a/b)=1

Limacon with inner loop

(a/b)<1

Dimpled limacon

1 < (a/b) < 2

How many petals if odd

n

How many petals if even (n ≥ 2)

2n

Where is at least one petal when its a cos graph

Pole or θ=0

Where is the initial petal in a sin graph

θ=pi/2/n

r=a cos(θ)

Circle with axis of sym on pole

r=a sin(θ)

Circle with axis of sym on θ=pi/2

r^2=a^2 sin(2θ)

Lemniscate with axis of sym from pi/2 by the distance of pi/2/n

r^2=a^2 cos(2θ)

Lemniscate with axis of sym on pole

How can you find the number of degrees between petals on a rose curve

2pi/number of petals

Ellipse

e (eccentricity) < 1

Parabola

e (eccentricity) = 1

Hyperbola

e (eccentricity) > 1

x^2+y^2

What is r^2 equal to

rcos(θ)

What is x equal to in polar form

rsin(θ)

What is y equal to in polar form

y/x

What is tan(θ) equal to

=k

How do you find the directix

Horizontal motion is

x=vtcos(θ)

Vertical motion is

vtsin(θ)-.5gt^2 +h