Polar graphs

θ=a

line

r=a

circle

r= a cos θ

circle on x axis

r= a sin θ

circle on y axis

r= a+b cos θ (a=b)

cardiod (x axis)

r= a+b sin θ (a=b)

cardiod (y axis)

r= -a-b cos θ (a>b)

no inner loop

r= a+b sin θ (a>b)

no inner loop

r= a+b sin θ (a

inner loop

r= a+b cos θ (a

inner loop

r= a cos(3θ)

three rose petal (symmetrical over x)

r= a sin (2θ)

4 petals (over y)

r= a cos(2θ)

4 petals (over x)

r=aθ

spiral

you only need to find angle between axis for what king of rose graph

sin rose graph

angle between petals

360/number of petals

angle between axis and petals

90/number of petals

in a rose graph number next to θ is

number of petals

in a rose graph the number in front of the rest of the equation is equal to

length of petals

conversion equations

y=rsinθ

x=rcosθ

r^2=x^2+y^2

tanθ=y/x

length of loop

b-a is always the negative if the graph is positive

length of rest (for loop)

b+a is always positive if the graph is positive

FOR A LIMACON AND CARDIOINAL GRAPHS ONLY and the odd number rose graphs (both sin and cos)

how do you know when it's negative

the b is negative

For axis circle graphs the radius is

A/2