Unit 5 Math Quiz Flashcards
Distance Formula (Polar Coordinates)
sqrt(r1^2 + r2^2 - 2r1r2 * cos(θ2-θ1))
Graphing: When r is negative, you graph…
Essentially, negative “x” =
(r, θ + π)
= Dial correctly, than reverse backwards
Graphing: When θ is negative, you essentially
Graph the mirror opposite of θ
Graphing: r = number
Circle around r value
Graphing: θ = radian
Line across positive and negative θ
Graphing: secθ
Vertical line?
What does symmetry to π/2 look like?
Symmetrical to “y-axis”
What does symmetry to the polar axis look like?
Symmetrical to “x-axis”
What does symmetry to the pole look like?
Diagonally symmetrical
r = aCosθ
r = aSinθ
Circle
r = a +/- bCosθ
r = a +/- bSinθ
Limacon
r = a +/- bCosθ
r = a +/- bSinθ
(a/b < 1)
Limacon with Inner Loop
r = a +/- bCosθ
r = a +/- bSinθ
(a/b = 1)
Cardinoid
r = a +/- bCosθ
r = a +/- bSinθ
(1< a/b < 2)
Dimpled Limacon
r = a +/- bCosθ
r = a +/- bSinθ
(a/b ≥ 2)
Convex Limacon
r = aCos#θ
r = aSin#θ
Rose
r = aCos3θ
3 Petals
r = aSin2θ
4 Petals
r = aSin5θ
5 Petals
r = aCos4θ
8 Petals
r^2 = a^2cos2θ
r^2 = a^2sin2θ
Lemniscates
r = aθ+b
Spirals of Archimedes
(r, θ) to (x,y)
x = rcosθ
y = rsinθ
(x,y) to (r, θ)
r = sqrt(x^2 + y^2)
θ = tan^-1(y/x)
