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both r=acosθ and r=asinθ
circle
passes through the origin
diameter = a
r=acosθ
x axis symmetry
a > 0 → center is (a/2,0); x int is (a,0)
a < 0 → center is (-a/2,0); x int is (-a,0)
r=asinθ
y axis symmetry
a > 0 → center is (0,a/2); y int is (0,a)
a < 0 → center is (0,-a.2); y int is (0,-a)
both r=acosnθ and r=asinnθ
length of petals = a
n = even → 2n petals
n = odd → n petals
petals are evenly spaced
period = 2pi/n
r=acosnθ
x axis symmetry
if a > 0, petal on positive x axis (a, 0)
if a < 0, petal on negative x axis (a, pi)
r=asinnθ
y axis symmettry
if a > 0, petal on pi/2n (a, pi/2n)
if a < 0, petal on -pi/2n (a, -pi/2n)
both r = a+bcosθ and r = a+bsinθ
sign of a = no effect
ignore signs
a < b → loop inside length = b-a
a = b → cardioid (heart shape)
a > b → becomes more circular— will not pass through the origin
r= a+bcosθ
x axis symmetry
b > 0 → symmetric on positive x axis
b < 0 → symmetric on negative x axis
ignore signs
one x intercept: b + a units from pole
y intercepts are a units away from pole
r= a+bsinθ
y axis symmetry
if b > 0 → symmetric on positive y axis
if b < 0 → symmetric on negative y axis
ignore signs
one y intercept: b+a units from pole
x intercepts are a units away from pole
both r=a+bcosnθ and r=a+bsinnθ
ignore signs
a < b →
n big petals (length = b+a)
n little petals (length = b-a)
n = odd → little petals inside big petals
n = even → little petals between big petals
a = b → n petals (length = b+a)
a > b → n petals but doesn’t go through pole (length = b+a)
shape becomes like a propeller
period = 2pi/n
r=a+bcosnθ
x axis symmetry
a < b
if b > 0, big petal on positive x axis
if b < 0, little petal on negative x axis
a = b or a > b
if b > 0 petal on positive x axis
if b < 0 and n = odd petal on negative x axis
if b > 0 and n = even, no petal on x axis
r=a+bsinnθ
θ=pi/2n symmetry
a < b or a = b or a > b
if b > 0, big petal on pi/2n
if b < 0, big petal on -pi/2n