# Worksheet: Polar Coordinates

In this worksheet, we will practice defining and plotting points given in polar coordinates and converting between the Cartesian and polar coordinates of a point.

**Q3: **

The polar coordinates of Point are . Which of the points , , , or is coincident with Point ?

- APoint
- BPoint
- CPoint
- DPoint

**Q4: **

Which of the ordered pairs
,
,
,
and
does **not** describe the position of Point in the diagram?

- A
- B
- C
- D

**Q5: **

Which of the ordered pairs
, ,
, and
does **not** describe the position of Point in the diagram?

- A
- B
- C
- D

**Q6: **

Which of the following ordered pairs does NOT describe the position of Point in the diagram?

- A
- B
- C
- D

**Q8: **

Consider the point with rectangular coordinates .

Calculate the distance of this point from the origin. Give your answer in exact form.

- A
- B
- C
- D
- E

Find the angle that makes with the positive -axis, giving your answer in radians to two decimal places.

- A
- B
- C
- D
- E

Given that point can be expressed in polar form as , which of the following is also a legitimate polar form for point ?

- A
- B
- C
- D
- E

**Q9: **

Answer the questions using the figure shown.

Which of the following are three possible pairs of polar coordinates for the marked point?

- A
- B
- C
- D
- E

What are the Cartesian coordinates of this point? Give these exactly.

- A
- B
- C
- D
- E

**Q10: **

William and Hannah are learning about polar coordinates. They have been given the point , which is , in polar coordinates, and the point , , in rectangular coordinates. They would like to compare these two points.

Hannah decides to convert point into rectangular coordinates. Determine the answer that Hannah will get.

- A
- B
- C
- D

William decides to convert point into polar coordinates. He does his calculations and gets an answer of . Is his answer correct?

- ANo
- BYes

William concludes that points and are different points, whereas Hannah concludes they are the same point. Who is correct?

- AHannah
- BWilliam

Which of the following statements represents a good learning point for William and Hannah as a result of this exercise?

- APolar coordinates are not unique representations for a point; there are many ways to express a point in polar coordinates.
- BRectangular coordinates are not unique representations for a point; there are many ways to express a point in rectangular coordinates.

**Q14: **

Consider the polar coordinates and , as shown in the figure.

Find the angle between the two lines.

- A
- B
- C

Use the law of cosines to find the length of . Give your answer accurate to three significant figures.

**Q15: **

Identify which of the points plotted on the graph has polar coordinates .

- A
- B
- C
- D
- E

**Q16: **

Consider the shown points.

Which one has the polar coordinates ?

- AC
- BE
- CA
- DD
- EB