6.4 Polar Equations

​6.4 Polar Equations

equation: r=asin(nθ),r=acos(nθ)

Facts:

for even values of n, the rose has 2n petals

for odd values of n, the rose has n petals

Roses!

equation: r=a±acosθ, r=a±asinθ

Facts:

length of the cardioid measured from the origin along the appropriate coordinate axis is 2a.

Cardioids

Sketching a Polar Curve

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Polar Curves

Multiple Choice

Choose the correct equation for the graph. #13

• $$r=3\ \cos\ \theta$$

• $$r\ =\ 3\ \sin\ \theta$$

• $$r\ =\ 3\ \cos\ 2\theta$$

• $$r\ =\ \sin\ 3\theta$$

Multiple Choice

Choose the correct equation for the graph. #14

• $$r=3\ \cos\ \theta$$

• $$r\ =\ 3\ \sin\ \theta$$

• $$r\ =\ 3\ \cos\ 2\theta$$

• $$r\ =\ \sin\ 3\theta$$

Multiple Choice

Choose the correct equation for the graph. #16

• $$r\ =\ 3$$

• $$r\ =\ \theta$$

• $$r\ =\ 7.5$$

• $$r\ =\ 3\theta$$

Multiple Choice

Choose the correct equation for the graph. #17

• $$r\ =\ 3$$

• $$r\ =\ \theta$$

• $$r\ =\ 7.5$$

• $$r\ =\ 3\theta$$

Multiple Choice

Identify the name of the polar graph: #2

• lemniscate

• rose curve

• cardioid

• sine curve

Multiple Choice

Determine the maximum r-value of the graph. #6

• 4

• 5

• 72

• 90

Multiple Choice

$$r=\cos\left[\left(3k\right)\theta\right]$$  is a rose curve.  What is the value of k if the graph has 12 petals? #7

• k = 1

• k = 2

• k = 3

• k = 4

Multiple Choice

Choose the correct equation for the graph. #12

• $$r\ =\ 0.5\ \sin\ 2\theta$$

• $$r\ =\ 0.5\ \cos\ 2\theta$$

• $$r\ =\ 3\ \sin\ 2\theta$$

• $$r\ =\ \sin\ 4\theta$$

Multiple Choice

Describe the curve. #29

• Rose with 4 leaves, Length 4

• Rose with 8 leaves, Length 4

• Cardioid with length 3

• Inner loop limacon with lengths 3 and 4

Multiple Choice

How many "petals" does the graph of $$r=8\cos9\theta$$  ? #32

• 9

• 18

• 8

• 17

Multiple Choice

Identify the name of the polar graph: #1

• lemniscate

• limacon

• cardioid

• circle centered at the pole

Multiple Choice

The polar graph is symmetric about _____. #5

• the polar axis

• the line $$\theta=\frac{\pi}{2}$$

• the pole

Multiple Choice

What is the equation for this graph? #26

• r² = 9cos2θ

• r² = 9sin2θ

• r² = 3cosθ

• r² = 3sinθ

Multiple Choice

Find the graph of the equation $$r^2=4\sin2\theta$$  #43

Multiple Choice

Identify the name of the polar graph: #3

• lemniscate

• rose curve

• cardioid

• limacon

Multiple Select

Describe the symmetry of the polar curve.

r = 7 cos 4θ

Select all that apply #23

• About the Pole

• Over polar axis

• Over θ=π/2

• No Polar Symmetry

Multiple Choice

What is the equation for this graph? #22

• r = 2 + sin θ

• r = 2 - sin θ

• r = 2 + cos θ

• r = 1 + 2sin θ

Multiple Choice

Which of these is an equation for this dimpled limaçon? #27

• r = 3 + 2 cosθ

• r = 2 + 3 cosθ

• r = 2 + 2cosθ

• r = 2 - 3cosθ