Free Printable Polar Number System

1.

Which point represents (3, 3π/4)?

a)

F

b)

E

c)

B

d)

A

2.

True or False: Polar Coordinates are unique?

a)

True

b)

False

c)

Made you look

d)

this quizizz rocks

3.

Which point represents the polar coordinate
(-4, -2π/3)?

a)

B

b)

F

c)

D

d)

A

4.

Convert the rectangular coordinates to polar form

a)

(√2 , 7π/4)

b)

(2 , 3π/4)

c)

(4 , π/4)

d)

(4 , 5π/4)

5.

Convert the polar coordinates to rectangular form

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

6.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

7.

Which equation represents the polar graph?

a)

r = sin θ

b)

r = sin 4θ

c)

r = 4 sin θ

d)

r = 4 cos θ

8.

Convert from polar coordinates, (6, 5π/4) to rectangular coordinates.

a)

(-3√2, -3√2)

b)

(3√2, 3√2)

c)

(6.0, 0.4)

d)

(-6.0, -0.4)

9.

Convert from polar coordinates, (20, 11π/6) to rectangular coordinates.

a)

(-10√3, 10)

b)

(10√3, -10)

c)

(10, -10√3)

d)

(10√2, -10)

10.

Convert the polar coordinates to rectangular coordinates.

a)

b)

c)

d)

11.

Covert the rectangular equation to polar form $x^2+y^2=9$

a)

r² = 81

b)

r = 3

c)

r = 4.5

d)

r sin θ = 9

12.

Covert the rectangular equation to polar form $y=x^2$

a)

r = cot θ csc θ

b)

r = tan θ csc θ

c)

r = tan θ sec θ

d)

r = 0

13.

What is the equation?

a)

Θ = π/4

b)

Θ = -5π/4

c)

Θ = -3π/4

d)

Θ = 5π/4

14.

What is the equation?

a)

r = 4

b)

r = 8

c)

r = 4sin(Θ)

d)

r = 8sin(Θ)

15.

Which equation represents the polar graph?

a)

r = 6 + 6 sin θ

b)

r = 12 sin θ

c)

r = 6 - 6 sin θ

d)

r = 6 + 6 cos θ

16.

4. Which polar equation graphs the same as
(x - 2)² + y²= 4

a)

r=4sinθ

b)

r=4cosθ

c)

r=2sinθ

d)

r=2cosθ

17.

Which one is the polar bear?

a)

b)

c)

d)

18.

Identify the polar equation:
r=1+sinθ

a)

cardioid

b)

circle

c)

limacon with inner loop

d)

spiral

19.

Match the correct polar equation with the following graph:

a)

r=1+cosθ

b)

rsinθ=2

c)

r=1-2sinθ

d)

r=2

20.

Classify the type of polar curve.

a)

Rose

b)

Cardiod

c)

Spiral of Archimedes

d)

Lemniscate

21.

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

22.

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

23.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

24.

Write the complex number in rectangular form

6 (cos 330 + i sin 330)

a)

$3\sqrt{3}+3i$

b)

$-3\sqrt{3}+3i$

c)

$3\sqrt{3}-3i$

d)

$-3\sqrt{3}-3i$

25.

4i Write the complex number in trig form $r\left(\cos\theta+i\sin\theta\right)$

a)

4(cos 270 + i sin 270)

b)

4 (cos 0 + i sin 0)

c)

4 (cos 90 + i sin 90)

d)

4 (cos 180 + i sin 180)

26.

Write the complex number in polar form

a)

√50 (cos π/2 + i sin π/2)

b)

50 (cos π/4 + i sin π/4)

c)

√50 (cos 5π/4 + i sin 5π/4)

d)

√50 (cos π/4 + i sin π/4)

27.

Find the indicated power using DeMoivre's Theorem

a)

72 - 72√3i

b)

- 72√3 + 72i

c)

- 72√2 + 72√2i

d)

-72 + 72√3i

28.

Write in rectangular form

a)

A

b)

B

c)

C

d)

D

29.

Write in polar form

a)

A

b)

B

c)

C

d)

D

30.

Find the square roots of 4√3 + 4i

SKIP THIS ONE

a)

2.705 + .725i and - 2.705 - .725i

b)

- 2.705 + .725i and 2.705 - .725i

c)

2.799 + .0128i and - 2.799 - .0128i

d)

- 2.799 + .0128i and 2.799 - .0128i

31.

Find
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form. Then express your final answer in rectangular form.

a)

-10

b)

10

c)

-10i

d)

10i

32.

Find
1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.

a)

√3/12 + 1/12 i

b)

12√3 + 12 i

c)

√3/12 - 1/12 i

d)

12√3 - 12i

33.

Find two additional representations of the given polar coordinates using -2π<θ<2π. Choose all that apply

a)

(3,-5π/6)

b)

(-3,π/6)

c)

(-3,-11π/6)

d)

(3,5π/6)

e)

(-3,-7π/6)

Polar Number System

Total questions: 33

Worksheet time: 4hrs 27mins

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