Free Printable Converting and Solving Polar Systems

1.

Which point represents (3, 3π/4)?

a)

F

b)

E

c)

B

d)

A

2.

How do you write an ordered pair?

a)

(X,X)

b)

(θ, r)

c)

(r,θ)

d)

(Y,Y)

3.

True or False: Polar Coordinates are unique?

a)

True

b)

False

4.

In the coordinate points (2,7⁰) the 2 represents the...

a)

theta

b)

directed distance

c)

x

d)

angle

5.

Which point represents (-4, 4π/3)

a)

F

b)

E

c)

B

d)

A

6.

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

a)

B

b)

F

c)

D

d)

A

7.

Which point represents (5, π)

a)

F

b)

E

c)

B

d)

A

8.

Which point represents (-4, π/2)

a)

D

b)

C

c)

B

d)

A

9.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

10.

Find the rectangular coordinates of each polar point. (4, 3π/2)

a)

(4,4)

b)

(4,0)

c)

(0,-4)

d)

(0,1)

11.

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)

12.

Find polar coordinates for the point:
(√3 , 1)

a)

(2, π/6)

b)

(-2, -π/6)

c)

(1,0)

d)

(4π,-2)

13.

When converting between rectangular and polar coordinates:

y = ?

a)

rcosθ

b)

rsinθ

c)

x² + y²

d)

y/x, x ≠ 0

14.

Convert the rectangular equation to a polar equation.
x²+y²=25

a)

r=5

b)

r=5sinΘ

c)

r=5cscΘ

d)

r=25

15.

Convert the rectangular equation to a polar equation.
3x²+3y²-48=0

a)

r=4

b)

r=48secΘ

c)

r=48cscΘ

d)

r=√48

16.

Convert the rectangular equation to a polar equation.
y=7

a)

r=7

b)

r=7sinΘ

c)

r=7cscΘ

d)

r=49

17.

Convert the polar equation to rectangular equation.
Θ=3π/4

a)

y=-x

b)

y=(-√2)x

c)

y=x

d)

y=-2x

18.

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

19.

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

20.

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)

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

21.

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)

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

22.

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

a)

b)

c)

d)

23.

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

a)

b)

c)

d)

24.

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

a)

b)

c)

d)

25.

Identify the polar equation:

r² = 9cos(2θ)

a)

lemniscate

b)

limacon with inner loop

c)

cardioid

d)

rose

26.

Identify the polar equation:
r=1+sinθ

a)

cardioid

b)

circle

c)

limacon with inner loop

d)

spiral

27.

Classify the type of polar curve.

a)

Rose

b)

Cardiod

c)

Spiral of Archimedes

d)

Lemniscate

Converting and Solving Polar Systems

Total questions: 27

Worksheet time: 1hrs 6mins

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