Polar Coordinates Worksheet

**Page 1**

1.

Which of the following is correct?

a. | Polar coordinate system is a line | ||

b. | Polar coordinate system is a Point | ||

c. | Polar coordinate system is a plane | ||

d. | Polar coordinate system is a space |

[Definition.]

Correct answer : (3)

2.

What is the number of coordinates of a point in a polar coordinate system?

a. | Infinite | ||

b. | 4 | ||

c. | 3 | ||

d. | 1 |

Correct answer : (1)

3.

What are the polar coordinates of the pole?

a. | ($\theta $, 0) | ||

b. | (0, 0) | ||

c. | (1, 2) | ||

d. | (0, $\theta $) |

Correct answer : (4)

4.

Which of the following is correct?

a. | Every point of a polar coordinate system has unique pair of polar coordinates. | ||

b. | Each pair of polar coordinates determine a unique point. | ||

c. | Every point of a polar coordinate system has 2 pairs of polar coordinates. | ||

d. | Each pair of polar coordinates does not determine a unique point. |

However, the polar coordinates of a point with directed distance

So, each pair of polar coordinates determine a unique point and for a point, the pairs of polar coordinates are not unique.

Correct answer : (2)

5.

From the polar coordinate system shown, the coordinates of P are

a. | (7, 60 ^{o}) | ||

b. | (5, 60 ^{o}) | ||

c. | (4, 60 ^{o}) | ||

d. | (6, 100 ^{o}) |

[From the figure.]

The measure of the angle made by the line OP with polar axis in the counter clockwise direction is 60

So, the polar coordinates of P are (5, 60

Correct answer : (2)

6.

The polar coordinates of point P are ($\sqrt{2}$, $\frac{\pi}{4}$). Which of the following are the rectangular coordinates for point P?

a. | (- 1, - 1) | ||

b. | (1, 1) | ||

c. | (- 1, 1) | ||

d. | (1, - 1) |

Let (

So,

(

Correct answer : (2)

7.

Let P be a point in a polar coordinate system. If $r$ is the directed distance from the pole O to P and $\theta $ is the directed angle measured in counter clockwise direction with the initial side on the polar axis and the terminal side on the line OP, then write the polar coordinates of P.

a. | (- $r$, $\theta $) | ||

b. | ($r$, $\theta $) | ||

c. | (- $\theta $, $r$) | ||

d. | ($\theta $, $r$) |

[Use the definition of directed distance.]

Here for P, the directed distance from the pole O is

The second polar coordinate of a point in a polar coordinate system is its directed angle whose initial side is on the polar axis and the terminal side is on the line OP.

[Use the definition of the directed angle.]

Here for P, the directed angle is

So, the polar coordinates of P are (

Correct answer : (2)

8.

The polar coordinates of a point P are ($r$, $\theta $). Which of the following is the polar coordinate pair of P other than ($r$, $\theta $)?

a. | ($r$, $\theta $ + $\frac{3\pi}{2}$) | ||

b. | ($r$, $\theta $ + 2$\pi $) | ||

c. | ($r$, $\theta $ + $\frac{\pi}{2}$) | ||

d. | ($r$, $\theta $ - $\frac{\pi}{2}$) |

For

So, among the choices, (

Correct answer : (2)

9.

Which of the following is correct?

a. | Both (2, $\frac{\pi}{6}$) and (2, $\frac{7\pi}{6}$) represent the same point. | ||

b. | Both (2, $\frac{\pi}{6}$) and (2, $\frac{13\pi}{6}$) do not represent the same point. | ||

c. | Both (2, $\frac{\pi}{6}$) and (2, $\frac{7\pi}{6}$) do not represent the same point. | ||

d. | Both (2, $\frac{\pi}{6}$) and (2, $\frac{13\pi}{6}$) represent the same point. |

Then (

[Substitute

(2,

[Write

So, both (2,

Correct answer : (4)

10.

Which of the following is correct?

a. | Both (3, $\frac{\pi}{3}$) and (- 3, $\frac{\pi}{3}$) represent the same point. | ||

b. | Both (3, $\frac{\pi}{3}$) and (- 3, - $\frac{\pi}{3}$) represent the same point. | ||

c. | Both (3, $\frac{\pi}{3}$) and (- 3, - $\frac{2\pi}{3}$) represent the same point. | ||

d. | Both (3, $\frac{\pi}{3}$) and (3, - $\frac{\pi}{3}$) represent the same point. |

So, (-

[Substitute

(-3, -

[Write -

So, both (3,

Correct answer : (3)