Polar to rectangular worksheet

A polar point gives you a distance and a direction. Dropping a perpendicular makes a right triangle whose legs are the rectangular coordinates, so x is r cos theta and y is r sin theta.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Polar to Rectangular Date Period Convert each point to rectangular form. Convert to rectangular: $(12, \frac{7 π}{4})$ Convert to rectangular: $(16, \frac{4 π}{3})$ Convert to rectangular: $(12, \frac{3 π}{2})$ Convert to rectangular: $(16, \frac{5 π}{3})$ Convert to rectangular: $(16, \frac{7 π}{6})$ Convert to rectangular: $(14, \frac{5 π}{4})$ Convert to rectangular: $(14, \frac{π}{3})$ Convert to rectangular: $(12, \frac{2 π}{3})$ Convert to rectangular: $(12, \frac{5 π}{4})$ Convert to rectangular: $(12, \frac{3 π}{4})$ Convert to rectangular: $(14, \frac{π}{6})$ Convert to rectangular: $(14, \frac{7 π}{4})$ Convert to rectangular: $(12, 0)$ Convert to rectangular: $(14, \frac{11 π}{6})$ Convert to rectangular: $(16, 0)$ Convert to rectangular: $(16, \frac{2 π}{3})$ Convert to rectangular: $(12, \frac{π}{3})$ Convert to rectangular: $(12, \frac{7 π}{6})$ Convert to rectangular: $(16, \frac{π}{3})$ Convert to rectangular: $(12, \frac{5 π}{3})$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Polar to Rectangular

Date Period

Convert each point to rectangular form.

Convert to rectangular: $(12, \frac{7 π}{4})$
Convert to rectangular: $(16, \frac{4 π}{3})$
Convert to rectangular: $(12, \frac{3 π}{2})$
Convert to rectangular: $(16, \frac{5 π}{3})$
Convert to rectangular: $(16, \frac{7 π}{6})$
Convert to rectangular: $(14, \frac{5 π}{4})$
Convert to rectangular: $(14, \frac{π}{3})$
Convert to rectangular: $(12, \frac{2 π}{3})$
Convert to rectangular: $(12, \frac{5 π}{4})$
Convert to rectangular: $(12, \frac{3 π}{4})$
Convert to rectangular: $(14, \frac{π}{6})$
Convert to rectangular: $(14, \frac{7 π}{4})$
Convert to rectangular: $(12, 0)$
Convert to rectangular: $(14, \frac{11 π}{6})$
Convert to rectangular: $(16, 0)$
Convert to rectangular: $(16, \frac{2 π}{3})$
Convert to rectangular: $(12, \frac{π}{3})$
Convert to rectangular: $(12, \frac{7 π}{6})$
Convert to rectangular: $(16, \frac{π}{3})$
Convert to rectangular: $(12, \frac{5 π}{3})$



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

Sigma Prep · sigmaprep.io/worksheets

Name

Polar to RectangularAnswer keyVersion 1

Date Period

Convert each point to rectangular form.

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

How to do these

Convert $(4, \frac{π}{3})$ to rectangular form

x is 4 cos of pi over 3, which is 4 times one half.
y is 4 sin of pi over 3, which is 4 times root 3 over 2.

The answer is $(2, 2 \sqrt{3})$ .

Where students go wrong

Pairing the wrong function with the wrong coordinate. x goes with cosine because the adjacent side lies along the x-axis. Swapping them reflects the point across the line y = x.

Also called converting polar to rectangular or polar to cartesian.

Questions about these worksheets

Yes. Every polar to rectangular 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.

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.

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.

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.

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.

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 to rectangular 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.

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.

Pairing the wrong function with the wrong coordinate. x goes with cosine because the adjacent side lies along the x-axis. Swapping them reflects the point across the line y = x.

Polar to rectangular worksheet

Select your difficulty

Polar to Rectangular

Polar to RectangularAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these polar to rectangular worksheets free?+

Do the polar to rectangular worksheets come with an answer key?+

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Can I get a different version of the same polar to rectangular worksheet?+

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