Polar Graphing Flashcards
Two polar coordinates for the same point (2 answers)
Add 2π to the angle
Flip the sign of r and add π to the angle
4 types of limacons
Looped
Cadioid
Dimpled
Convex
Looped
b>a
Cardioid
a=b
Dimpled
a>b (close in value)
Convex
a»b (much greater)
General form of a limacon
r=a+/- b sinθ
r=a+/- b cosθ
Length of a loop in a looped limacon
2(b-a)
Depth of a dimple
2b
Converting rectangular to polar substitutions
x=r cos θ
y=r sin θ
x² + y² = r²
Converting a polar point with negative r (radians) to positive r
Flip the sign of r
(-r,θ) -> (r,θ)
Add pi/3.14 to theta
Horizontal/vertical slopes
use x= rcosθ and y=rsinθ
substitute into x and y
find which is a constant
Usually no slope; slope = 0
tan
sinθ/cosθ
sec
1/cosθ
csc
1/sinθ
cot
cosθ/sinθ
Circle location
r=a; (0,0)
r=acos θ; (a/2,0)
r= asin θ; (0,a/2)
Circle Radius
a/2
Circle length
2πr
Rose cos
Number of petals:
N is odd = n
Even = 2n
length: a
First petal: 0 degrees
angle between: 360/number of petals
Rose sin
Number of petals: same
length: same
1st petal: 90/n
Angle between: 360/number of petals
Looped limacon
Location: x or y axis
cos: x-axis
sin: y-axis
Inner loop length: b-a
Maximum r: a+b
Minimum; a-b
Dimpled limacon
Location:
Cos: x-axis
Sin: y-axis
Length of dimple: 2a-b
Maximum r = a+b
Convex limacon
Location: same
length of convex portion: a-b
Max r : a+b
