Free Printable POLAR GRAPHING - Week 7

1.

Describe the graph of the Polar equation.

$r\ =\ 4\sin\left(3\theta\right)$

a)

Rose with 3 petals

b)

Rose with 6 petals

c)

Limacon with loop

d)

Circle

2.

Describe the graph of the Polar equation.

$r\ =\ 9\cos\left(6\theta\right)$

a)

Circle

b)

Rose with 6 petals

c)

Rose with 12 petals

d)

Limacon with Inner loop

3.

Describe the graph of the Polar equation.

$r\ =\ 3\ -\ 3\sin\theta$

a)

Rose with 3 petals

b)

Circle

c)

Cardioid

d)

Limacon with Inner loop

4.

Describe the graph of the Polar equation.

$r\ =\ 5\cos\left(9\theta\right)$

a)

Circle with a diameter of 5

b)

Rose with 18 petals and length 5

c)

Rose with 5 petals and length 9

d)

Rose with 9 petals and length 5

5.

Describe the graph of the Polar equation.

$r\ =\ 3\sin\left(4\theta\right)$

a)

Rose with 4 petals

b)

Rose with 8 petals

c)

Cardioid

d)

Limacon with Inner loop

6.

Describe the graph of the Polar equation:
$r\ =\ 1\ +\ \sin\theta$

a)

Cardioid

b)

Circle

c)

Limacon with inner loop

d)

Convex Limacon

7.

Describe the graph of the Polar equation:
$r\ =\ 1\ -\ 3\cos\theta$

a)

Limacon with inner loop

b)

Dimpled Limacon

c)

Rose

d)

Cardiod

8.

Describe the graph of the Polar equation:

$r\ =\ 6\ +\ 2\cos\theta$

a)

Limacon with Inner loop

b)

Dimpled Limacon

c)

Cardiod

d)

Convex Limacon

9.

Classify the type of Polar graph.

a)

Rose

b)

Cardiod

c)

Dimpled Limacon

d)

Lemniscate

10.

Which of the following equations is a "Cardioid"?

a)

$r=4-4\cos\theta$

b)

$r=3+7\sin\theta$

c)

$r=3-2\sin\theta$

d)

$r=1-2\cos\theta$

11.

Which of the following equations is a "Limacon with Inner loop"?

a)

$r=4-4\cos\theta$

b)

$r=3+7\sin\theta$

c)

$r=3-2\sin\theta$

d)

$r=1-\cos\theta$

12.

How many "petals" are contained in the graph of the given equation?

$r=8\cos\left(10\theta\right)$

a)

16

b)

10

c)

20

d)

8

13.

How many "petals" are contained in the graph of the given equation?

$r=8\cos\left(9\theta\right)$

a)

9

b)

18

c)

8

d)

17

14.

Which is the equation of a Rose curve that contains 100 petals?

a)

$r=100\cos100\theta$

b)

$r=6\sin50\theta$

c)

$r=25\sin75\theta$

d)

$r=10\cos10\theta$

15.

Given the equation $r=7\cos\left(4\theta\right)$ if the "4" is changed to "5" to get $r=7\cos\left(5\theta\right)$ , then what change takes 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

16.

What makes $r=a-b\cos\theta$ a cardioid limacon?

a)

when $a\ge2b$

b)

when a > b

c)

when a = b

d)

when b < a < 2b

17.

Identify the ZEROS of the given equation.

$r\ =\ 1\ -\ 2\sin\theta$

a)

$\frac{\pi}{6},\frac{5\pi}{6}$

b)

$\frac{\pi}{3},\frac{2\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{7\pi}{6},\frac{11\pi}{6}$

18.

What is the difference between the polar graphs of $r\ =\ 2\ +\ 6\cos\theta$ and
$r\ =\ 2\ -\ 6\cos\theta$ ?

a)

Both are Horizontal, but one points right while the other points left

b)

Both are Vertical, but one points up while the other points down

c)

One is Horizontal while the other is Vertical

d)

They are the same

19.

For the given equation, which is the corresponding graph?

a)

b)

c)

d)

20.

What is the polar equation of the provided graph?

a)

r = 4

b)

$r=4\theta$

c)

$\theta=4$

d)

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

21.

What is the polar equation of the provided graph?

a)

$r\ =\ 4\sin\theta$

b)

$r\ =\ -2\sin\theta$

c)

$r\ =\ 2\cos\theta$

d)

$r\ =\ -4\cos\theta$

22.

What is the polar equation of the provided graph?

a)

$r\ =\ 3\cos\theta$

b)

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

c)

$r\ =\ 3\sin\theta$

d)

$r\ =\ -3\sin\theta$

23.

What is the polar equation of the provided graph?

a)

$r\ =\ \sin\left(4\theta\right)$

b)

$r\ =\ 6\sin\left(2\theta\right)$

c)

$r\ =\ 6\cos\left(4\theta\right)$

d)

$r\ =\ \cos\left(4\theta\right)$

24.

What is the polar equation of the provided graph?

a)

$r\ =\ 4\cos\left(5\theta\right)$

b)

$r\ =\ 5\sin\left(4\theta\right)$

c)

$r\ =\ 5\cos\left(8\theta\right)$

d)

$r\ =\ 5\cos\left(4\theta\right)$

25.

What is the polar equation of the provided graph?

a)

$r\ =\ 2\cos\left(7\theta\right)$

b)

$r\ =\ 7\sin\left(14\theta\right)$

c)

$r\ =\ 2\sin\left(7\theta\right)$

d)

$r\ =\ 2\sin\left(14\theta\right)$

26.

What is the polar equation of the provided graph?

a)

$r\ =\ 3\sin\left(4\theta\right)$

b)

$r\ =\ 3\cos\left(4\theta\right)$

c)

$r\ =\ 3\sin\left(8\theta\right)$

d)

$r\ =\ 3\cos\left(8\theta\right)$

27.

What is the polar equation of the provided graph?

a)

$r\ =\ 7\cos\left(8\theta\right)$

b)

$r\ =\ 8\cos\left(7\theta\right)$

c)

$r\ =\ 7\sin\left(16\theta\right)$

d)

none of these

28.

What is the polar equation of the provided graph?

a)

$r=9-\cos\theta$

b)

$r=2-8\cos\theta$

c)

$r=3+7\sin\theta$

d)

$r=4-6\cos\theta$

29.

What is the polar equation of the provided graph?

a)

$r\ =\ 3\ +\ 2\cos\theta$

b)

$r\ =\ 2\ +\ 3\cos\theta$

c)

$r\ =\ 2\ +\ 2\cos\theta$

d)

$r\ =\ 3\cos\theta$

30.

What is the polar equation of the provided graph?

a)

$r\ =\ 6\ +\ 6\sin\theta$

b)

$r\ =\ 12\sin\theta$

c)

$r\ =\ 4\ -\ 3\sin\theta$

d)

$r\ =\ 4\ +\ 5\sin\theta$

31.

What is the polar equation of the provided graph?

a)

$r\ =\ 3\ +\ 2\cos\theta$

b)

$r\ =\ 2\ +\ 3\cos\theta$

c)

$r\ =\ 2\ +\ 2\cos\theta$

d)

$r\ =\ 2\ -3\cos\theta$

32.

What is the polar equation of the provided graph?

a)

$r\ =\ 1\ +\ \cos\theta$

b)

$r\ =\ 2\sin\theta$

c)

$r\ =\ 1\ -\ 2\sin\theta$

d)

$r\ =\ 2$

33.

For the given equation, identify the SHAPE of the Polar graph:

$r\ =\ 5\ \sin\left(2\theta\right)$

a)

Cardiod

b)

Limacon with Inner Loop

c)

Convex Limacon

d)

Rose

34.

For the given equation, identify the Number of Petals of the graph:

$r\ =\ 5\sin\left(2\theta\right)$

a)

2

b)

4

c)

5

d)

10

35.

For the given equation, identify the Max r-value of the graph:

$r\ =\ 5\sin\left(2\theta\right)$

a)

2

b)

4

c)

5

d)

10

36.

For the given equation, identify the Number of ZEROS of the graph:

$r\ =\ 5\sin\left(2\theta\right)$

a)

3

b)

4

c)

5

d)

6

37.

For the given equation, which of the following is NOT a significant point on the graph:

$r\ =\ 5\sin\left(2\theta\right)$

a)

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

b)

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

c)

$\left(5,\ \frac{7\pi}{4}\right)$

d)

$\left(5,\ \frac{\pi}{2}\right)$

38.

For the Rose curve with the given equation, what is the SPACING ANGLE (the angle between petals)?

$r\ =\ 5\sin\left(2\theta\right)$

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$\frac{3\pi}{2}$

d)

$\frac{\pi}{4}$

39.

For the given equation, identify the SHAPE of the Polar graph:

$r\ =\ 2\ -\ 3\cos\theta$

a)

Cardiod

b)

Limacon with Inner Loop

c)

Convex Limacon

d)

Rose

40.

For the given equation, identify the Max r-value of the graph:

$r\ =\ 2\ -\ 3\cos\theta$

a)

2

b)

3

c)

5

d)

6

41.

For the given equation, identify the Number of ZEROS of the graph:

$r\ =\ 2\ -\ 3\cos\theta$

a)

1

b)

2

c)

3

d)

4

42.

For the given equation, which of the following is NOT a significant point on the graph:

$r\ =\ 2\ -3\cos\theta$

a)

$\left(-1,\ 0\right)$

b)

$\left(1,\ 0\right)$

c)

$\left(5,\ \pi\right)$

d)

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

43.

For the given equation, identify the SHAPE of the Polar graph:

$r\ =\ 5\ \cos\left(3\theta\right)$

a)

Cardiod

b)

Limacon with Inner Loop

c)

Convex Limacon

d)

Rose

44.

For the given equation, identify the Number of Petals of the graph:

$r\ =\ 5\cos\left(3\theta\right)$

a)

3

b)

5

c)

6

d)

10

45.

For the given equation, identify the Max r-value of the graph:

$r\ =\ 5\cos\left(3\theta\right)$

a)

3

b)

5

c)

6

d)

10

46.

For the given equation, identify the Number of ZEROS of the graph:

$r\ =\ 5\cos\left(3\theta\right)$

a)

3

b)

4

c)

5

d)

6

47.

For the given equation, which of the following is NOT a significant point on the graph:

$r\ =\ 5\cos\left(3\theta\right)$

a)

$\left(5,\ 0\right)$

b)

$\left(5,\ \frac{2\pi}{3}\right)$

c)

$\left(5,\ \frac{5\pi}{6}\right)$

d)

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

48.

For the Rose curve with the given equation, what is the SPACING ANGLE (the angle between petals)?

$r\ =\ 5\cos\left(3\theta\right)$

a)

$\frac{\pi}{2}$

b)

$\frac{2\pi}{3}$

c)

$\frac{3\pi}{2}$

d)

$\pi$

POLAR GRAPHING - Week 7 - LATE

Total questions: 48

Worksheet time: 4hrs 41mins

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