Polar Coordinates Flashcards
1
Q
x =
A
r cos θ
2
Q
y =
A
r sin θ
3
Q
x^2 + y^2 =
A
r^2
4
Q
θ =
A
arctan (y/x)
5
Q
r = a
A
a circle center O, radius r in polar form
6
Q
θ = α
A
a half-line through O and making an angle α with the initial line
7
Q
r = α θ
A
a spiral starting at O
8
Q
Area under a curve between lines θ = α and θ = β?
A
1/2 ∫ r^2 dθ using α and β as limits
9
Q
tangent parallel to initial line?
A
dy/dθ = 0
10
Q
tangent perpendicular to the initial line?
A
dx/dθ = 0
11
Q
egg shape occurs when?
A
r = a (p + q cos θ)
p ≥ 2q
12
Q
dimple shape?
A
r = a (p + q cos θ)
q ≤ p < 2q
