Free Printable Polar Graphs and Rectangular Conversion

1.

Which letter represents the point

(-4,\frac{4π}{3})

?

a)

F

b)

E

c)

B

d)

A

2.

Which coordinates land at point A? CHOOSE ALL THAT APPLY!

a)

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

b)

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

c)

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

d)

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

3.

Convert the polar point into rectangular form:

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

a)

$(1,1)$

b)

$(1,-1)$

c)

$(-1,0)$

d)

$(-1,-1)$

4.

This is a _____ ____.

(a)

5.

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)

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

6.

Write the polar equation into a rectangular equation?
r=2sinΘ+2cosΘ

a)

x²+y²=2x+2y

b)

r=2x+2y

c)

r=x²+y²

d)

x²-y²=2x-2y

7.

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)

$r=-4\theta$

8.

Convert to a rectangular equation: $r=4\cos\theta+5\sin\theta$

a)

$\sqrt{x^2+y^2}+4x-5y=0$

b)

$\sqrt{x^2+y^2}-4x-5y=0$

c)

$x^2+y^2-4x-5y=0$

d)

$x^2+y^2-5x-4y=0$

9.

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)

$\theta=\pi$

10.

What movie is this?

(a)

11.

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

12.

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

13.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

14.

What is the equation?

a)

r = 4

b)

r = 8

c)

r = 4sin(Θ)

d)

r = 8sin(Θ)

15.

This particular equation generates what graph

a)

b)

c)

d)

16.

What is the equation for this graph?

a)

$r=6\sin\theta$

b)

$r=-6\sin\theta$

c)

$r=6\cos\theta$

d)

$r=-6\cos\theta$

17.

What is the polar equation of the graph shown here?

a)

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

b)

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

c)

$\theta=\pi$

d)

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

18.

Identify the equation in the polar graph

a)

$r\ =7+4\sin\theta$

b)

$r\ =\ 7+4\cos\theta$

c)

$r\ =\ 4+7\sin\theta$

d)

$r\ =4+7\cos\theta$

19.

What is the equation?

a)

r = 4sin(Θ)

b)

r = -2sin(Θ)

c)

r = 2cos(Θ)

d)

r = -4cos(Θ)

20.

a)

$r=5+2\cos\theta$

b)

$r=2+5\cos\theta$

c)

$r=3+4\cos\theta$

d)

$r=4+3\cos\theta$

e)

$r=7\cos\theta$

21.

This refers to the presence of distinct and opposite charges or orientations, such as the positive and negative poles of a magnet or the positive and negative terminals of a battery. It's a fundamental concept in understanding the behavior of electromagnetic fields and interactions

(a)

22.

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)

$r=5\cos8\theta$

e)

$r=5\sin4\theta$

23.

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

a)

r = 2cos(7θ)

b)

r = 7sin(14θ)

c)

r = 2sin(7θ)

d)

r = 2sin(14θ)

e)

r = 2sin(3.5θ)

24.

The petals of the graph of $r=5\sin\left(4\theta\right)$ will be at intervals of

a)

$30\degree$

b)

$45\degree$

c)

$60\degree$

d)

$90\degree$

25.

Which input creates the end of the first petal of the graph of $r=8\sin\left(3\theta\right)$ .

a)

0

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{2}$

d)

$\frac{\pi}{6}$

26.

Which is the FIRST input value that creates the endpoint of the last petal of $r=2\sin\left(7\theta\right)$ when graphing in order from $0\ to\ 2\pi$

a)

$\frac{\pi}{14}$

b)

$\frac{13\pi}{14}$

c)

$\frac{27\pi}{14}$

d)

$\frac{5\pi}{14}$

e)

$\frac{11\pi}{14}$

27.

Which input creates the end of the third petal of the graph of $r=4\sin\left(3\theta\right)$ when graphing in order from $0\ to\ \pi$

a)

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

b)

$\frac{3\pi}{4}$

c)

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

d)

$\frac{11\pi}{12}$

28.

Which interval creates the loop (highlighted) of

r = 2 + 4 cosθ

a)

$\left[0,\frac{\pi}{3}\right]$

b)

$\left[\frac{\pi}{3},\ \frac{2\pi}{3}\right]$

c)

$\left[\frac{2\pi}{3},\ \frac{4\pi}{3}\right]$

d)

$\left[\frac{4\pi}{3},\ \frac{5\pi}{3}\right]$

e)

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

Polar Graphs and Rectangular Conversion

Total questions: 28

Worksheet time: 21mins

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