Polar coordinates worksheet

Q: Are these polar coordinates worksheets free?

Yes. Every polar coordinates sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Q: Do the polar coordinates worksheets come with an answer key?

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Q: Are these polar coordinates worksheets printable?

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Q: What grade are these polar coordinates worksheets for?

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Q: Can I get a different version of the same polar coordinates worksheet?

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

Q: Is this a free alternative to Kuta Software for polar coordinates?

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the polar coordinates questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Q: Can I choose how hard the polar coordinates questions are?

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Q: What kinds of question are on a polar coordinates worksheet?

You pick from 3: polar to rectangular, rectangular to polar and another pair for the same point. Tick as many as you want and set how many of each, or let it spread them evenly.

A polar point says how far out and which way round, instead of how far across and how far up. Converting is just the two right-triangle relationships, so every angle here is one you already know exactly.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Polar Coordinates Date Period Convert each point. Leave answers exact. Convert to rectangular: $(12, \frac{7 π}{4})$ Convert to polar, angle in radians: $(- 16, 0)$ Convert to rectangular: $(12, \frac{3 π}{2})$ Convert to polar, angle in radians: $(- 8 \sqrt{3}, - 8)$ Convert to rectangular: $(16, \frac{7 π}{6})$ Convert to polar, angle in radians: $(- 7 \sqrt{3}, 7)$ Convert to rectangular: $(14, \frac{π}{3})$ Convert to polar, angle in radians: $(6, 6 \sqrt{3})$ Convert to rectangular: $(12, \frac{5 π}{4})$ Convert to polar, angle in radians: $(- 8 \sqrt{2}, 8 \sqrt{2})$ Convert to rectangular: $(12, \frac{3 π}{4})$ Convert to polar, angle in radians: $(14, 0)$ Convert to rectangular: $(16, \frac{5 π}{3})$ Convert to polar, angle in radians: $(0, 12)$ Convert to rectangular: $(14, \frac{7 π}{4})$ Convert to polar, angle in radians: $(0, - 12)$ Convert to rectangular: $(14, \frac{11 π}{6})$ Convert to polar, angle in radians: $(0, - 16)$ Convert to rectangular: $(16, \frac{2 π}{3})$ Convert to polar, angle in radians: $(6 \sqrt{2}, 6 \sqrt{2})$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Polar Coordinates

Date Period

Convert each point. Leave answers exact.

Convert to rectangular: $(12, \frac{7 π}{4})$
Convert to polar, angle in radians: $(- 16, 0)$
Convert to rectangular: $(12, \frac{3 π}{2})$
Convert to polar, angle in radians: $(- 8 \sqrt{3}, - 8)$
Convert to rectangular: $(16, \frac{7 π}{6})$
Convert to polar, angle in radians: $(- 7 \sqrt{3}, 7)$
Convert to rectangular: $(14, \frac{π}{3})$
Convert to polar, angle in radians: $(6, 6 \sqrt{3})$
Convert to rectangular: $(12, \frac{5 π}{4})$
Convert to polar, angle in radians: $(- 8 \sqrt{2}, 8 \sqrt{2})$
Convert to rectangular: $(12, \frac{3 π}{4})$
Convert to polar, angle in radians: $(14, 0)$
Convert to rectangular: $(16, \frac{5 π}{3})$
Convert to polar, angle in radians: $(0, 12)$
Convert to rectangular: $(14, \frac{7 π}{4})$
Convert to polar, angle in radians: $(0, - 12)$
Convert to rectangular: $(14, \frac{11 π}{6})$
Convert to polar, angle in radians: $(0, - 16)$
Convert to rectangular: $(16, \frac{2 π}{3})$
Convert to polar, angle in radians: $(6 \sqrt{2}, 6 \sqrt{2})$



Sigma Prep · sigmaprep.io/worksheets Name Polar CoordinatesAnswer keyVersion 1 Date Period Convert each point. Leave answers exact. Convert to rectangular: $(12, \frac{7 π}{4})$ $(6 \sqrt{2}, - 6 \sqrt{2})$ Convert to polar, angle in radians: $(- 16, 0)$ $(16, π)$ Convert to rectangular: $(12, \frac{3 π}{2})$ $(0, - 12)$ Convert to polar, angle in radians: $(- 8 \sqrt{3}, - 8)$ $(16, \frac{7 π}{6})$ Convert to rectangular: $(16, \frac{7 π}{6})$ $(- 8 \sqrt{3}, - 8)$ Convert to polar, angle in radians: $(- 7 \sqrt{3}, 7)$ $(14, \frac{5 π}{6})$ Convert to rectangular: $(14, \frac{π}{3})$ $(7, 7 \sqrt{3})$ Convert to polar, angle in radians: $(6, 6 \sqrt{3})$ $(12, \frac{π}{3})$ Convert to rectangular: $(12, \frac{5 π}{4})$ $(- 6 \sqrt{2}, - 6 \sqrt{2})$ Convert to polar, angle in radians: $(- 8 \sqrt{2}, 8 \sqrt{2})$ $(16, \frac{3 π}{4})$ Convert to rectangular: $(12, \frac{3 π}{4})$ $(- 6 \sqrt{2}, 6 \sqrt{2})$ Convert to polar, angle in radians: $(14, 0)$ $(14, 0)$ Convert to rectangular: $(16, \frac{5 π}{3})$ $(8, - 8 \sqrt{3})$ Convert to polar, angle in radians: $(0, 12)$ $(12, \frac{π}{2})$ Convert to rectangular: $(14, \frac{7 π}{4})$ $(7 \sqrt{2}, - 7 \sqrt{2})$ Convert to polar, angle in radians: $(0, - 12)$ $(12, \frac{3 π}{2})$ Convert to rectangular: $(14, \frac{11 π}{6})$ $(7 \sqrt{3}, - 7)$ Convert to polar, angle in radians: $(0, - 16)$ $(16, \frac{3 π}{2})$ Convert to rectangular: $(16, \frac{2 π}{3})$ $(- 8, 8 \sqrt{3})$ Convert to polar, angle in radians: $(6 \sqrt{2}, 6 \sqrt{2})$ $(12, \frac{π}{4})$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Polar CoordinatesAnswer keyVersion 1

Date Period

Convert each point. Leave answers exact.

Convert to rectangular: $(12, \frac{7 π}{4})$ $(6 \sqrt{2}, - 6 \sqrt{2})$
Convert to polar, angle in radians: $(- 16, 0)$ $(16, π)$
Convert to rectangular: $(12, \frac{3 π}{2})$ $(0, - 12)$
Convert to polar, angle in radians: $(- 8 \sqrt{3}, - 8)$ $(16, \frac{7 π}{6})$
Convert to rectangular: $(16, \frac{7 π}{6})$ $(- 8 \sqrt{3}, - 8)$
Convert to polar, angle in radians: $(- 7 \sqrt{3}, 7)$ $(14, \frac{5 π}{6})$
Convert to rectangular: $(14, \frac{π}{3})$ $(7, 7 \sqrt{3})$
Convert to polar, angle in radians: $(6, 6 \sqrt{3})$ $(12, \frac{π}{3})$
Convert to rectangular: $(12, \frac{5 π}{4})$ $(- 6 \sqrt{2}, - 6 \sqrt{2})$
Convert to polar, angle in radians: $(- 8 \sqrt{2}, 8 \sqrt{2})$ $(16, \frac{3 π}{4})$
Convert to rectangular: $(12, \frac{3 π}{4})$ $(- 6 \sqrt{2}, 6 \sqrt{2})$
Convert to polar, angle in radians: $(14, 0)$ $(14, 0)$
Convert to rectangular: $(16, \frac{5 π}{3})$ $(8, - 8 \sqrt{3})$
Convert to polar, angle in radians: $(0, 12)$ $(12, \frac{π}{2})$
Convert to rectangular: $(14, \frac{7 π}{4})$ $(7 \sqrt{2}, - 7 \sqrt{2})$
Convert to polar, angle in radians: $(0, - 12)$ $(12, \frac{3 π}{2})$
Convert to rectangular: $(14, \frac{11 π}{6})$ $(7 \sqrt{3}, - 7)$
Convert to polar, angle in radians: $(0, - 16)$ $(16, \frac{3 π}{2})$
Convert to rectangular: $(16, \frac{2 π}{3})$ $(- 8, 8 \sqrt{3})$
Convert to polar, angle in radians: $(6 \sqrt{2}, 6 \sqrt{2})$ $(12, \frac{π}{4})$

How to do these

Convert to rectangular: $(6, \frac{5 π}{6})$

x is 6 cos of 5 pi over 6, and cosine there is negative root 3 over 2.
That gives x equals negative 3 root 3.
y is 6 sin of 5 pi over 6, which is 6 times one half.

The answer is $(- 3 \sqrt{3}, 3)$ .

Where students go wrong

Giving one answer for a polar point. Every point has infinitely many names: add a full turn, or flip the sign of r and turn half way round, and you land in the same place. A question asking for another pair is asking you to use that.

Also called polar and rectangular coordinates, converting coordinates or polar form of a point.

What you can put on this worksheet

Polar to rectangular: Convert to rectangular: $(6, 12 0^{\circ})$ → $(- 3, 3 \sqrt{3})$
Rectangular to polar: Convert to polar, angle in degrees: $(- 6, 0)$ → $(6, 18 0^{\circ})$
Another pair for the same point: Another pair, with $r < 0$ : $(6, 12 0^{\circ})$ → $(- 6, 30 0^{\circ})$

Questions about these worksheets