# Worksheet: Conversion between Polar and Rectangular Coordinates

In this worksheet, we will practice using the transformation equations relating polar and Cartesian coordinates to convert points from polar to rectangular coordinates.

**Q2: **

Convert to polar coordinates. Give the angle in radians and round to three significant figures throughout.

- A
- B
- C
- D

**Q3: **

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

**Q4: **

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

**Q5: **

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?

- AYes
- BNo

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

- AWilliam
- BHannah

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

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

**Q6: **

Convert to polar coordinates. Give the angle in degrees and round to three significant figures throughout.

- A
- B
- C
- D