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Polars
polar shiznit
23
Mathematics
11th Grade
04/12/2011
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Term
4 things to remember
 Definition
x^2 + y^2 = r^2, rcosø=x, rsinø=y, tanø = y/x
Term
all possibilities of polar (x,ø)
 Definition
(x,ø) + 2πn / (-x, π+ø) + 2πn
Term
r=acos(nø) (what is a?)
 Definition
ROSE (a = length)
Term
n = odd
 Definition
n petals
Term
n = even
 Definition
2n petals
Term
ROSE = positive cos
 Definition
odd = one petal on +x, even = petals on all axis
Term
ROSE = positive sin
 Definition
odd = one petal on -y axis, even = no petals on axis
Term
ROSE = negative (even vs odd)
 Definition
even = only order changes, odd = shift over x for sin and y for cos
Term
period of rose
 Definition
odd = π, even = 2π
Term
period of circle
 Definition
π
Term
period of weirdo's
 Definition
2π
Term
r=a+/-B(sin/cos)ø
 Definition
Limacon (and cardoid)
Term
sin (usual position, symmetry, negative sign)
 Definition
usually on positive y axis, symmetry on y axis, negative sign means flip over x axis
Term
cos (usual position, symmetry, negative sign)
 Definition
usually on positive x axis, symmetry on x axis, negative means flip over y
Term
a/b < 1
 Definition
inner loop
Term
a/b = 1
 Definition
cardiod (bumbum)
Term
a/b between 1 and 2
 Definition
dimpled limacon (lima bean)
Term
a/b≥2
 Definition
convex limacon(oval?)
Term
limacon max value
 Definition
addition or subtraction of a and b (work around negative)
Term
inner loop
 Definition
smallest possible a+-b
Term
r=asinø
 Definition
circle, a=diameter (on positive y)
Term
r=acosø
 Definition
circle, a=diameter, (on positive x)
Term
r=-a(sin/cos)xø
 Definition
circle, diameter a, on negative y or negative x axis
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