# 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.

Q1:

Consider the points plotted on the graph.

Write down the polar coordinates of , giving the angle in the range .

• A
• B
• C
• D
• E

Q2:

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

• APoint
• BPoint
• CPoint
• DPoint

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

Q7:

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

• 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.

Q11:

Given that the polar coordinates of point are , find the Cartesian coordinates of .

• A
• B
• C
• D

Q12:

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

• A
• B
• C
• D

Q13:

Find the distance between the polar coordinates and . Give your answer accurate to three significant figures.

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