Degrees and radians worksheet for Precalculus

In Precalculus radians become the default unit, because arc length and the graphs of the trig functions are built on them. Conversions here include negative angles and angles beyond a full turn, and some add a follow-up step, like adding 2π or comparing the result with 180°.

Also taught in Algebra 2, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Degrees and Radians Date Period Convert each angle, then give the coterminal or reference angle asked for. Convert degrees to radians Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 20^{\circ}$ Convert to radians, then give its reference angle in radians: $195^{\circ}$ Convert to radians, then give its reference angle in radians: $- 70^{\circ}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $486^{\circ}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $530^{\circ}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 665^{\circ}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $850^{\circ}$ Convert to radians, then give its reference angle in radians: $- 10^{\circ}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 702^{\circ}$ Convert to radians, then give its reference angle in radians: $365^{\circ}$ Convert radians to degrees Convert to degrees, then give its reference angle in degrees: $\frac{25 π}{18}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{57 π}{10}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{9 π}{10}$ Convert to degrees, then give its reference angle in degrees: $- \frac{17 π}{10}$ Convert to degrees, then give its reference angle in degrees: $- \frac{π}{5}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{7 π}{5}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{5}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{18}$ Convert to degrees, then give its reference angle in degrees: $\frac{28 π}{9}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{31 π}{12}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Degrees and Radians

Date Period

Convert each angle, then give the coterminal or reference angle asked for.

Convert degrees to radians
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 20^{\circ}$
Convert to radians, then give its reference angle in radians: $195^{\circ}$
Convert to radians, then give its reference angle in radians: $- 70^{\circ}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $486^{\circ}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $530^{\circ}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 665^{\circ}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $850^{\circ}$
Convert to radians, then give its reference angle in radians: $- 10^{\circ}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 702^{\circ}$
Convert to radians, then give its reference angle in radians: $365^{\circ}$

Convert radians to degrees
Convert to degrees, then give its reference angle in degrees:
$\frac{25 π}{18}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{57 π}{10}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{9 π}{10}$
Convert to degrees, then give its reference angle in degrees:
$- \frac{17 π}{10}$
Convert to degrees, then give its reference angle in degrees:
$- \frac{π}{5}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{7 π}{5}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{5}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{18}$
Convert to degrees, then give its reference angle in degrees:
$\frac{28 π}{9}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{31 π}{12}$



Sigma Prep · sigmaprep.io/worksheets Name Degrees and RadiansAnswer keyVersion 2 Date Period Convert each angle, then give the coterminal or reference angle asked for. Convert degrees to radians Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 20^{\circ}$ $- \frac{π}{9}$ ; $\frac{17 π}{9}$ Convert to radians, then give its reference angle in radians: $195^{\circ}$ $\frac{13 π}{12}$ ; $\frac{π}{12}$ Convert to radians, then give its reference angle in radians: $- 70^{\circ}$ $- \frac{7 π}{18}$ ; $\frac{7 π}{18}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $486^{\circ}$ $\frac{27 π}{10}$ ; $\frac{7 π}{10}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $530^{\circ}$ $\frac{53 π}{18}$ ; $\frac{17 π}{18}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 665^{\circ}$ $- \frac{133 π}{36}$ ; $\frac{11 π}{36}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $850^{\circ}$ $\frac{85 π}{18}$ ; $\frac{13 π}{18}$ Convert to radians, then give its reference angle in radians: $- 10^{\circ}$ $- \frac{π}{18}$ ; $\frac{π}{18}$ Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 702^{\circ}$ $- \frac{39 π}{10}$ ; $\frac{π}{10}$ Convert to radians, then give its reference angle in radians: $365^{\circ}$ $\frac{73 π}{36}$ ; $\frac{π}{36}$ Convert radians to degrees Convert to degrees, then give its reference angle in degrees: $\frac{25 π}{18}$ $250^{\circ}$ ; $70^{\circ}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{57 π}{10}$ $1026^{\circ}$ ; $306^{\circ}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{9 π}{10}$ $- 162^{\circ}$ ; $198^{\circ}$ Convert to degrees, then give its reference angle in degrees: $- \frac{17 π}{10}$ $- 306^{\circ}$ ; $54^{\circ}$ Convert to degrees, then give its reference angle in degrees: $- \frac{π}{5}$ $- 36^{\circ}$ ; $36^{\circ}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{7 π}{5}$ $- 252^{\circ}$ ; $108^{\circ}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{5}$ $- 36^{\circ}$ ; $324^{\circ}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{18}$ $- 10^{\circ}$ ; $350^{\circ}$ Convert to degrees, then give its reference angle in degrees: $\frac{28 π}{9}$ $560^{\circ}$ ; $20^{\circ}$ Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{31 π}{12}$ $465^{\circ}$ ; $105^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Degrees and RadiansAnswer keyVersion 2

Date Period

Convert each angle, then give the coterminal or reference angle asked for.

Convert degrees to radians
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 20^{\circ}$ $- \frac{π}{9}$ ; $\frac{17 π}{9}$
Convert to radians, then give its reference angle in radians: $195^{\circ}$ $\frac{13 π}{12}$ ; $\frac{π}{12}$
Convert to radians, then give its reference angle in radians: $- 70^{\circ}$ $- \frac{7 π}{18}$ ; $\frac{7 π}{18}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $486^{\circ}$ $\frac{27 π}{10}$ ; $\frac{7 π}{10}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $530^{\circ}$ $\frac{53 π}{18}$ ; $\frac{17 π}{18}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 665^{\circ}$ $- \frac{133 π}{36}$ ; $\frac{11 π}{36}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $850^{\circ}$ $\frac{85 π}{18}$ ; $\frac{13 π}{18}$
Convert to radians, then give its reference angle in radians: $- 10^{\circ}$ $- \frac{π}{18}$ ; $\frac{π}{18}$
Convert to radians, then give the coterminal angle in $[0, 2 π)$ : $- 702^{\circ}$ $- \frac{39 π}{10}$ ; $\frac{π}{10}$
Convert to radians, then give its reference angle in radians: $365^{\circ}$ $\frac{73 π}{36}$ ; $\frac{π}{36}$

Convert radians to degrees
Convert to degrees, then give its reference angle in degrees:
$\frac{25 π}{18}$ $250^{\circ}$ ; $70^{\circ}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{57 π}{10}$ $1026^{\circ}$ ; $306^{\circ}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{9 π}{10}$ $- 162^{\circ}$ ; $198^{\circ}$
Convert to degrees, then give its reference angle in degrees:
$- \frac{17 π}{10}$ $- 306^{\circ}$ ; $54^{\circ}$
Convert to degrees, then give its reference angle in degrees:
$- \frac{π}{5}$ $- 36^{\circ}$ ; $36^{\circ}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{7 π}{5}$ $- 252^{\circ}$ ; $108^{\circ}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{5}$ $- 36^{\circ}$ ; $324^{\circ}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $- \frac{π}{18}$ $- 10^{\circ}$ ; $350^{\circ}$
Convert to degrees, then give its reference angle in degrees:
$\frac{28 π}{9}$ $560^{\circ}$ ; $20^{\circ}$
Convert to degrees, then give the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $\frac{31 π}{12}$ $465^{\circ}$ ; $105^{\circ}$

How to do these

Convert to degrees, then give its reference angle:
$- \frac{7 π}{9}$

Multiply by 180 over pi; the pi cancels: -7 × 180 ÷ 9 = -140.
-140° is coterminal with 220°, which is in Quadrant III.
Reference angle: 220° - 180° = 40°.

The answer is $- 140^{\circ}$ ; $40^{\circ}$ .

Where students go wrong

Changing the angle while converting it. -195° is -13π/12, not 165° turned into radians: a conversion changes the unit only, so the sign and the number of turns stay the same.

Also called converting degrees to radians, radian measure or angle measure.

What you can put on this worksheet

Degrees to radians: Convert to radians the central angle of a sector: $210^{\circ}$ → $\frac{7 π}{6}$
Radians to degrees: Convert to degrees:
$\frac{7 π}{6}$ → $210^{\circ}$
Negative angles: Convert to radians: $- 210^{\circ}$ → $- \frac{7 π}{6}$

Questions about these worksheets

Yes. Every degrees and radians 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 degrees and radians 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 three 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.

You pick from 3: degrees to radians, radians to degrees and negative angles. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying by the wrong fraction. Going to radians the 180 is underneath, going to degrees it is on top. A quick sanity check: a radian answer should be a smallish number times pi, and a degree answer should not have pi in it at all.

Degrees and radians worksheet for Precalculus

Select your difficulty

Convert degrees to radians

Convert radians to degrees

Convert degrees to radians

Convert radians to degrees

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these degrees and radians worksheets free?+

Do the degrees and radians worksheets come with an answer key?+

Are these degrees and radians worksheets printable?+

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Can I get a different version of the same degrees and radians worksheet?+

Is this a free alternative to Kuta Software for degrees and radians?+

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What do students get wrong with degrees and radians?+