Chapter 9 -> Polar Coordinates Math

r=acosθ a>0

(Circle)Symmetric to Polar Axis

r=asinθ a>0

(Circle) Symmetric to θ=π/2

r=acosθ a<0

(Circle) Symmetric to Polar Axis

r=asinθ a<0

(Circle) Symmetric to θ=π/2

r=a+bsinθ

(Limacon) opens up

r=a-bsinθ

(Limacon) opens down

r=a+bcosθ

(Limacon) opens right

r=a-bcosθ

(Limacon) opens left

a/b<1

Limacon w/ a inner loop

a/b=1

Cardioid

2>a/b>1

Dimpled Limacon

a/b greater than or equal to 2

convex limacon

How do you solve for maxes?

set r equal to the greatest possible r value and solve

Ex:

How do you solve for zeros?

set r equal to the 0 and solve

Ex:

r^2=a^2cos(2θ)

(Lemniscates) Symmetric to Polar Axis

r^2=a^2sin(2θ)

(Lemniscates) Symmetric to pole

r=aθ+b θ>0

(Spirals of Archimedes) Starts from the top (Graph w/ table of values)

r=aθ+b θ<0

(Spirals of Archimedes) Starts from the bottom (Graph w/ table of values)

r=acos(nθ) r=asin(nθ) n is odd

n # of petals

r=acos(nθ) r=asin(nθ) n is even

2n # of petals