Free Printable POLAR graphs

1.

Match the correct polar equation with the following graph:

a)

r=1+cosθ

b)

rsinθ=2

c)

r=1-2sinθ

d)

r=2

2.

Identify the polar equation:
r=1+sinθ

a)

cardioid

b)

circle

c)

limacon with inner loop

d)

spiral

3.

Which point represents (2, π/6)

a)

F

b)

E

c)

B

d)

A

4.

Classify the type of polar curve.

a)

Rose

b)

Cardiod

c)

Spiral of Archimedes

d)

Lemniscate

5.

Which of the following could be the equation for...

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 6 - 6 sin θ

d)

r = 6 + 6 cos θ

6.

Convert the rectangular equation to polar form

a)

r² = 81

b)

r = 3

c)

r = 4.5

d)

r sin θ = 9

7.

Choose a correct equation for the red circle.

a)

r = -3

b)

r = -3sinΘ

c)

r = -3cosΘ

d)

x² + y² = 3

8.

Choose a correct equation for the blue circle.

a)

r = 2

b)

r = 4

c)

r = 2sinΘ

d)

x² + y² = 2

9.

Which of these is an equation for this dimpled limaçon?

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 2 - 3cosθ

10.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

11.

What is the equation?

a)

Θ = π/4

b)

Θ = -5π/4

c)

Θ = -3π/4

d)

Θ = 5π/4

12.

Identify the polar equation:
r=1-3cosθ

a)

Limacon with inner loop

b)

Limacon without inner loop

c)

rose

d)

spiral

13.

True or False: Polar Coordinates are unique? In other words, each point on a polar grid only has one way to write its coordinates.

a)

True

b)

False

c)

Made you look

d)

this quizizz rocks

14.

Match the given polar equation with its corresponding graph.

r^2=9\cos2\theta

a)

rose

b)

lemniscate

c)

dimpled limacon

d)

cardioid

15.

Match the given polar equation with its corresponding graph.

$r=5\cos2\theta$

a)

rose

b)

lemniscate

c)

dimpled limacon

d)

cardioid

16.

Match the given polar equation with its corresponding graph.

$r=2-3\cos\theta$

a)

cardioid

b)

dimpled limacon

c)

inner loop limacon

d)

flat limacon

17.

Match the given polar equation with its corresponding graph.

$r=5+4\cos\theta$

a)

dimpled limacon

b)

cardioid

c)

inner loop limacon

d)

flat limacon

18.

Match the given polar equation with its corresponding graph.

$r=-3-3\cos\theta$

a)

dimpled limacon

b)

cardioid

c)

flat limacon

d)

inner loop limacon

19.

Match the given polar equation with its corresponding graph.

$r=-2$

a)

Line passing through origin

b)

circle with center NOT at (0,0)

c)

spiral

d)

circle with center AT (0,0)

20.

Match the given polar equation with its corresponding graph.

$r\ =\ 2\theta$

a)

lemniscate

b)

spiral

c)

flat limacon

d)

line

21.

Match the given polar equation with its corresponding graph.

$\theta=\frac{2\theta}{3}$

a)

spiral

b)

limacon

c)

line passing through the origin

d)

cardioid

22.

Rewrite the following from rectangular form into polar form.

y = - 4

a)

$r=-\frac{4}{\cos\theta}$

b)

$r=-\frac{4}{\sin\theta}$

c)

$r=\frac{4}{\sin\theta}$

d)

$r=-4\theta$

23.

Rewrite the following polar equation into rectangular form.

$r=\frac{4}{3\cos\theta+7\sin\theta}$

a)

$7x+3y\ =\ 4$

b)

$y=\frac{4}{7}x-\frac{3}{7}$

c)

$7x-3y\ =\ 4$

d)

$y=-\frac{3}{7}x+\frac{4}{7}$

24.

The polar equation r = 7, when graphed, is a ...

a)

line through the origin

b)

circle centered at origin

c)

hyperbola orientated vertically

d)

none of your business

25.

What is the polar equation of the graph shown here?

a)

$\theta=-\frac{\pi}{4}$

b)

$\theta=\frac{\pi}{3}$

c)

$\theta=\pi$

d)

$\theta=\frac{\pi}{6}$

26.

Which polar equation is equivalent to the rectangular equation $y=x$ ?

a)

$\theta=-\frac{\pi}{3}$

b)

$\theta=\frac{\pi}{6}$

c)

$\theta=\frac{\pi}{4}$

d)

$\theta=\pi$

27.

What does the polar function look like? $r=\theta$

a)

a spiral

b)

a circle

c)

a line

d)

a rose

28.

How many "petals" does the graph of $r=8\cos10\theta$

a)

16

b)

10

c)

20

d)

8

29.

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

a)

9

b)

18

c)

8

d)

17

30.

Which equation is represented by the graph?

a)

$r=4\sin5\theta$

b)

$r=2.5\sin5\theta$

c)

$r=5\cos4\theta$

d)

$r=4\cos5\theta$

31.

Which equation below has 100 petals?

a)

$r=100\cos100\theta$

b)

$r=6\sin50\theta$

c)

$r=25\sin75\theta$

d)

$r=10\cos10\theta$

32.

Which is NOT true about the rose function
$r=7\sin6\theta$ ?

a)

Each petals is less than 10 units long

b)

There are more than 7 petals

c)

There are fewer than 11 petals

d)

It is symmetrical about the y-axis

33.

In the equation $r=7\cos4\theta$ if I changed the 4 to a 5 to get $r=7\cos5\theta$ , then what change took place in the graph?

a)

the amount of petals would decrease

b)

the amount of petals would increase

c)

the length of each petal would increase

d)

the length of each petal would decrease

34.

$r=5\cos n\theta$

Based on the graph shown find the value of n.

(a)

35.

$r=A\cos n\theta$ Based on the graph shown, find the value of A + n. (Both A and n are integers)

(a)

36.

$r=A\cos n\theta$ Based on the graph shown, find the value of A + n. (Both A and n are integers)

(a)

37.

$r=A\cos n\theta$ Based on the graph shown, find the value of A + n. (Both A and n are integers)

(a)

38.

Which of these is the equation of the graph shown?

a)

$r=5\cos4\theta$

b)

$r=5\sin5\theta$

c)

$r=4\cos8\theta$

d)

$r=5\cos8\theta$

39.

Which equation represents the graph shown?

a)

$r=5\cos6\theta$

b)

$r=5\cos5\theta$

c)

$r=5\sin7\theta$

d)

none of these

40.

Which equation represents the graph shown?

a)

$r=7\cos8\theta$

b)

$r=8\cos7\theta$

c)

$r=7\sin16\theta$

d)

none of these

41.

Which equation represents the graph shown?

a)

$r=3\cos3\theta$

b)

$r=10\sin3\theta$

c)

$r=7\sin3\theta$

d)

none of these

42.

Find the distance between two points $\left(-2,\frac{\pi}{3}\right),\left(3,\frac{2\pi}{3}\right)$

a)

4.36

b)

4.84

c)

2.65

d)

1.61

43.

Three of the following coordinates represent the same point. Which one represents a DIFFERENT point from the others?

a)

$\left(4,\frac{\pi}{3}\right)$

b)

$\left(4,-\frac{5\pi}{3}\right)$

c)

$\left(-4,\frac{5\pi}{3}\right)$

d)

$\left(-4,-\frac{2\pi}{3}\right)$

44.

Convert to a polar equation $3x+7y=9$

a)

$r=\frac{9}{\cos3\theta+\sin7\theta}$

b)

$r=\frac{9}{7\cos\theta+3\sin\theta}$

c)

$r=\frac{9}{3\cos\theta+7\sin\theta}$

d)

$r=\frac{9}{7\cos3\theta+3\sin7\theta}$

45.

Convert to a polar equation $y^2-4x=0$

a)

$r=4\cos\theta\sin^2\theta$

b)

$r=4\cot\theta\csc\theta$

c)

$r=4\sin\theta\cos^2\theta$

d)

$r=4\cot\theta\sec\theta$

46.

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

a)

b)

c)

d)

47.

Find the graph of the equation $r=-4\theta$

a)

b)

c)

d)

48.

Find the graph of the equation $r=7\cos4\theta$

a)

b)

c)

d)

49.

Find the graph of the equation $r=8\sin\theta$

a)

b)

c)

d)

50.

Find the graph of the equation $r=2\sin3\theta$

a)

b)

c)

d)

51.

What is the equation?

a)

r = 4

b)

r = 8

c)

r = 4sin(Θ)

d)

r = 8sin(Θ)

52.

What is the equation?

a)

r = 4sin(Θ)

b)

r = -2sin(Θ)

c)

r = 2cos(Θ)

d)

r = -4cos(Θ)

53.

The graph of r = 3 - 5cos(Θ) is a limacon with an inner loop. What is the diameter of the outer and inner loops?

a)

Outer Loop: 8, Inner Loop: 2

b)

Outer Loop: 4, Inner Loop: 1

c)

Outer Loop: 16, Inner Loop: 4

d)

Outer Loop: 15, Inner Loop: 2

54.

What kind of graph will you get from r = 2 + 6cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod (heart)

d)

A circle

55.

What kind of graph will you get from the equation r = 6 + 2cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod

d)

A line

56.

What kind of graph will you get from the equation r = 2 + 2cos(Θ)?

a)

A limacon with an inner loop

b)

A dimpled limacon

c)

A cardiod

d)

A flower

57.

What is the difference between the polar graphs of r = 2 + 6cos(Θ) and

r = 2 - 6cos(Θ)?

a)

Both are on the x-axis, but one faces right while the other faces left

b)

Both are on the y-axis, but one faces up while the other faces down

c)

One is on the x-axis while the other is on the y-axis

d)

They are the same!

58.

This particular equation generates what graph

a)

b)

c)

d)

59.

Which equation represents the polar graph?

a)

r = sin 4θ

b)

r = 6 sin 2θ

c)

r = 6 cos 4θ

d)

r = cos 4θ

60.

Choose a correct equation for this rose curve.

a)

r = sin(7θ)

b)

r = 7sin(2θ)

c)

r = 2sin(7θ)

d)

r = 2sin(14θ)

61.

Identify the polar equation:

r = 4sin(5θ)

a)

rose

b)

lemniscate

c)

spiral

d)

circle

62.

Identify the polar equation:

r² = 9cos(2θ)

a)

lemniscate

b)

limacon with inner loop

c)

cardioid

d)

rose

63.

Which equation represents the polar graph?

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 4 - 3 sin θ

d)

r = 4 + 5 sin θ

64.

Describe the curve

a)

Cardioid

b)

Circle

c)

Inner loop limacon

d)

Rose with 6 leaves

65.

The following equation would graph what shape?

a)

3 leaf rose

b)

6 leaf rose

c)

2 leaf rose

d)

4 leaf rose

66.

Determine the polar equation of the given graph.

a)

r² = -9sin(2θ)

b)

r² = 9cos(2θ)

c)

r² = -9cos(2θ)

d)

r² = 9sin(2θ)

67.

Describe the curve

a)

Rose with 4 leaves

b)

Rose with 8 leaves

c)

Cardioid

d)

Inner loop limacon

68.

Describe the curve

a)

Rose with 3 leaves

b)

Rose with 6 leaves

c)

Inner loop limacon

d)

Circle

69.

Describe the curve

a)

Rose with 3 leaves

b)

Circle

c)

Cardioid

d)

Inner loop limacon

70.

Describe the curve

a)

Circle

b)

Rose with 6 leaves

c)

Rose with 12 leaves

d)

Inner loop limacon

71.

Describe the curve

a)

Circle

b)

Cardioid

c)

Rose with 5 leaves

d)

Rose with 9 leaves

72.

The graph is an example of

a)

Spiral of Archimedes

b)

Logarithmic Spiral

c)

Spiral of Antiquity

d)

Limax Spiral

73.

Write the equation of a limacon with an inner loop of length 3 and an outer loop of length 7, symmetric to the y axis.

a)

r = 2 + 5sin(θ)

b)

r = 3 + 7sin(θ)

c)

r = 2 - 5cos(θ)

d)

r = 3 - 7cos(θ)

74.

Identify the polar equation:

r = 2θ

a)

spiral

b)

rose

c)

cardioid

d)

lemniscate

75.

What is the equation for this graph?

a)

r² = 9cos2θ

b)

r² = 9sin2θ

c)

r² = 3cosθ

d)

r² = 3sinθ

76.

What is the equation for this graph?

a)

$r=2+2\cos\theta$

b)

$r=4+4\cos\theta$

c)

$r=2+2\sin\theta$

d)

$r=3+1\cos\theta$

e)

$r=2-2\cos\theta$

77.

What is the equation for this graph?

a)

$r=3-3\sin\theta$

b)

$r=3-3\cos\theta$

c)

$r=6-6\sin\theta$

d)

$r=6-6\cos\theta$

e)

$r=6\sin\theta$

78.

What is the equation for this graph?

a)

$r=3+2\sin\theta$

b)

$r=2+3\sin\theta$

c)

$r=3+2\cos\theta$

d)

$r=3-2\sin\theta$

e)

$r=5+5\cos\theta$

79.

What is the equation for this graph?

a)

$r=2-6\sin\theta$

b)

$r=6-2\cos\theta$

c)

$r=6-2\sin\theta$

d)

$r=2-6\cos\theta$

e)

$r=6\cos\left(-2\theta\right)$

80.

What is the equation for this graph?

a)

$r=3+5\sin\theta$

b)

$r=3+5\cos\theta$

c)

$r=5+3\sin\theta$

d)

$r=5+3\cos\theta$

e)

$r=3-5\cos\theta$

81.

What is the equation for this graph?

a)

$r=2\sin7\theta$

b)

$r=7\sin2\theta$

c)

$r=2\cos7\theta$

d)

$r=7\cos2\theta$

e)

$r=2+7\cos\theta$

82.

What is the equation for this graph?

a)

$r^2=16\cos2\theta$

b)

$r^2=16\sin2\theta$

c)

$r=4\cos2\theta$

d)

$r=4\sin2\theta$

e)

$r^2=4\sin2\theta$

83.

What is the equation for this graph?

a)

$r=\theta$

b)

$r=2\theta$

c)

$r=1$

d)

$r=-\theta$

e)

$r=-2\theta$

84.

What is the equation for this graph?

a)

$r=\theta$

b)

$r=5\cos\theta$

c)

$r=5$

d)

$r=\theta+5$

e)

$\theta=5$

85.

What type of polar equation is graphed?

a)

Lemniscate

b)

Cardioid

c)

Limacon

d)

Rose

e)

Spiral

86.

What type of graph would this following equation make?
$r=3\theta+1$

a)

Spiral

b)

Line

c)

Circle

d)

Rose

e)

Cardioid

87.

What type of graph would this polar equation make?
$r^2=25\cos\left(2\theta\right)$

a)

Lemniscate

b)

Spiral

c)

Rose

d)

Limacon

e)

Circle

88.

$r=10\sin\left(5\theta\right)$ What type of graph would this polar equation make?

a)

Rose

b)

Lemniscate

c)

Spiral

d)

Circle

e)

Line

89.

What type of graph would this polar equation make?

$r=8-5\sin\theta$

a)

Limacon with an inner loop

b)

Limacon without an inner loop

c)

Lemniscate

d)

Rose

e)

Cardioid

90.

What type of graph would this polar equation make?
$r=9\sin\theta$

a)

Line

b)

Circle

c)

Cardioid

d)

Rose

e)

Spiral

91.

What type of graph would this polar equation make?
$r\sin\theta=7$

a)

Line

b)

Circle

c)

Cardioid

d)

Rose

e)

Spiral

POLAR graphs

Total questions: 91

Worksheet time: 5hrs 22mins

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