Precalculus - 9.1-9.2 Quiz

types of polar graphs

1. circle

2. limacon

3. rose

4. lemniscate

5. spiral of archimedes

circles

r = acosθ (left/right)

r = asinθ (up/down)

|a| is diameter

limacon with inner loop graph

limacon with inner loop equation

a < b

r = a—bsinθ

a + b is diameter thing

roses

r = acos nθ

r = asin nθ

where n > 2 is an integer

|a| is petal length

r = asin nθ (even n)

r = asin nθ (odd n)

r = acos nθ (even n)

r = acos nθ (odd n)

how many petals does a rose have?

n petals if n is odd

2n petals if n is even

dimpled limacon equation

b < a < 2b

r = a—bcosθ

a + b is diameter thing

cardioid/dimpled limacon graph

cardioid equation

a = b

r = a + bcosθ

2a is diameter thing

convex limacon equation

a > 2b

r = a + b sinθ

a + b is diameter thing

convex limacon graph

lemniscates

r² = a²cos2θ

r² = a²sin2θ

|a| is length of petal

r² = a²cos2θ

r² = a²sin2θ

x =

rcosθ

y =

rsinθ

spirals of archimedes

r = aθ + b

θ > 0 (start on top)

θ < 0 (start on bottom)

spiral when θ > 0

spiral when θ < 0

r² =

x² + y²

tanθ

y/x

distance formula

r = (sq. rt.)(r₁ + r₂ - 2r₁,r₂cos(θ₂—θ₁)

tanθ

y/x

right circle

a > 0

left circle

a < 0

up circle

a > 0

down circle

a < 0