Free Printable Polar Points, Equations, and Graphs

1.

Match the correct polar equation with the following graph:

a)

r = 1 + cosθ

b)

rsinθ = 2

c)

r = 1+ sinθ

d)

r = 2

2.

Identify the polar equation:

r= 0.5θ

a)

cardioid

b)

circle

c)

limacon with inner loop

d)

spiral

3.

Which point represents $\left(2,\frac{\pi}{6}\right)$ ?

a)

F

b)

E

c)

B

d)

A

4.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

5.

How do you write an ordered pair in polar coordinates?

a)

(X, Y)

b)

(θ, r)

c)

(r, θ)

d)

(y, x)

6.

Find the rectangular coordinates of polar coordinates $\left(4,\frac{3\pi}{2}\right)$

a)

( 4, 4 )

b)

( 4, 0 )

c)

( 0, - 4 )

d)

( 0, 1)

7.

Convert the rectangular equation to polar form

a)

r² = 81

b)

r = 3

c)

r = 4.5

d)

r sin θ = 9

8.

Choose a correct equation for the red circle.

a)

r = -3

b)

r = -3sinΘ

c)

r = -3cosΘ

d)

x² + y² = 3

9.

Choose a correct equation for the blue circle.

a)

r = 2

b)

r = 4

c)

r = 2sinΘ

d)

x² + y² = 2

10.

Which of these equations is a vertical line ?

a)

r = 4

b)

r = $\frac{2}{\sin\theta}$

c)

r = $\frac{2}{\cos\theta}$

d)

r = 2 - 3cosθ

11.

Choose the correct equation.

a)

r = 3 + 2 cosθ

b)

r = 2 + 3 cosθ

c)

r = 2 + 2cosθ

d)

r = 3cosθ

12.

What is the equation?

a)

Θ = $\frac{\pi}{4}$

b)

Θ = $\frac{-5\pi}{4}$

c)

Θ = $\frac{-3\pi}{4}$

d)

Θ = $\frac{5\pi}{4}$

13.

Convert the rectangular coordinates to polar form $\left(-\sqrt{6},\ -\sqrt{2}\right)$

a)

( $2\sqrt{2}$ , $\frac{7\pi}{6}$ )

b)

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

c)

( $2\sqrt{2}$ , $\frac{\pi}{6}$ )

d)

(8 , $\frac{7\pi}{6}$ )

14.

Convert the polar coordinates to rectangular form $\left(\sqrt{2},\ -\frac{\pi}{4}\right)$

a)

(1, 1)

b)

(1, -1)

c)

(-1, 0)

d)

(-1, -1)

15.

Covert the rectangular equation to polar form $y=4$

a)

r sin θ = 4

b)

r = 4 cosθ

c)

r = sinθ/4

d)

r = 4 sinθ

16.

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

a)

B

b)

F

c)

D

d)

A

17.

Which equation represents the polar graph?

a)

r = sin 4θ

b)

r = 6 sin 2θ

c)

r = 6 cos 2θ

d)

r = cos 4θ

18.

Which rectangular equation is the same as r = 6sinƟ

a)

x²+ y² = 9

b)

(x - 3)² + y² = 9

c)

x² + ( y - 3 )² = 9

d)

x² + y² = 9

19.

Which one of the following is an equation for r = 4cosθ

a)

x² + y² = 16

b)

(x + 2)² + y² = 4

c)

(x - 2)² + y² = 4

d)

x² + ( y - 2 )² = 4

20.

What are the coordinates of the center and radius of the circle whose equation is r = - 8sinθ

a)

center ( 0, 0) and r = 4

b)

center ( - 4, 0 ) and r = 4

c)

center ( 0, 4) and r = 4

d)

center ( 0, - 4) and r = 4

21.

Which point is at the same location as point A (7, $\frac{4\pi}{3}$ ) ?

a)

( 7, $\frac{\pi}{3}$ )

b)

( -7, $\frac{\pi}{3}$ )

c)

( -7, $-\frac{\pi}{3}$ )

d)

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

22.

Which point is at the same location as point P $\left(-6,\ -30\degree\right)?$

a)

$\left(6,\ 30\degree\right)$

b)

$\left(-6,\ -390\degree\right)$

c)

$\left(6,\ -30\degree\right)$

d)

$\left(-6,\ 150\degree\right)$

23.

Which polar point with $r\ge0\ and\ 0\le\theta\le2\pi$ is equivalent to the rectangular point ( 4, - 4 )?

a)

$\left(4\sqrt{2},\ \frac{7\pi}{4}\right)$

b)

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

c)

$\left(-4\sqrt{2},\ \frac{7\pi}{4}\right)$

d)

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

24.

Which one is the rectangular equation for $\theta=\frac{5\pi}{6}$ ?

a)

y = $\sqrt{3}x$

b)

y = - $\sqrt{3}x$

c)

y = $\frac{\sqrt{3}}{3}x$

d)

y = $\frac{-\sqrt{3}}{3}x$

25.

What are the polar coordinates with $r\le0\ and\ 0\le\theta\le360\degree$ for the rectangular point P ( 0, - 23 ) ?

a)

$\left(-23,\ 180\degree\right)$

b)

$\left(-23,\ 270\degree\right)$

c)

$\left(-23,\ -90\degree\right)$

d)

$\left(-23,\ 90\degree\right)$

Polar Points, Equations, and Graphs

Total questions: 25

Worksheet time: 26mins

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