PRECALC Polar Equations

r=a

Circle centered at origin… a= the ring number of the circle

θ=k

A line through (0,0) with an angle of k˚ in relation to the positive x-axis

rsinθ=a

Horizontal line at y=a

rcosθ=a

Vertical line at x=a

r=acosθ

Circle centered on x axis

C=(1/2a,0)

R= |1/2a|

r=asinθ

C=(0, 1/2a)

R= |1/2a|

r=acosnθ

a “Rose”

if n is even, 2n petals… if n odd, n petals

the first petal at 0˚ if a>0 and at 180˚ if a<0

# of degrees between petals is 360/#of petals

petal length= |a|

r=asin(nθ)

a “Rose”

if n is even, 2n petals, if n odd, n petals

first petal at 90˚/n

# of degrees between petals is 360/#of petals

petal lengh= |a|

r= a ± a cosθ

Cardioid around the x axis and through the origin

if a>0, elongated right |2a| units

if a<0, elongated left |2a| units

BASICALLY— length= |a|, width = |2a|…

r= a ± a sinθ

cardioid around the y axis and through the origin

if a>0, elongated up |2a|

if a<0 elongated down |2a|

left/right |a|
basically length |2a|, width |a|

r= a± b cos θ, a=/b

Limacon around the x axis

if |a|<|b| there is a loop

if |a|>|b| there is no loop

PLUS SIGN elongates right
NEGATICE SIGN elongates left

r= a± b sin θ, a=/b

Limacon around the y axis

if |a|<|b| there is a loop

if |a|>|b| there is no loop

PLUS SIGN elongates up
NEGATICE SIGN elongates down

r² = a² sin 2θ

Lemniscate in Q1 and Q3
petal length= [a]

r² = a² cos 2θ

lemniscated on the x axis

petal length |a|