List four angles between 0° and 720°, one in each quadrant, with reference angle 20°

For example: 20°, 340°, 520°, 560°

Coterminal and reference angles worksheet for Precalculus

Precalculus mixes degrees and radians, and the angles are often negative or more than one full turn. Reduce first to an angle between 0 and 360° or 0 and 2π, then read the quadrant and the reference angle from that, ready for the unit circle.

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 Coterminal and Reference Angles Date Period Answer each question. Find a coterminal angle Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $960^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 750^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 690^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $945^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 1035^{\circ}$ Find the reference angle What is the reference angle of $- 495^{\circ}$ ? Find the reference angle of $435^{\circ}$ . An angle of $1245^{\circ}$ is in standard position. Find its reference angle. What is the reference angle of $770^{\circ}$ ? Find the reference angle of $- 170^{\circ}$ . Find a coterminal angle in radians Find the coterminal angle in $[0, 2 π)$ : $\frac{19 π}{3}$ Find the coterminal angle in $[0, 2 π)$ : $- \frac{15 π}{2}$ Find the coterminal angle in $[0, 2 π)$ : $8 π$ Find the coterminal angle in $[0, 2 π)$ : $- 3 π$ Find the coterminal angle in $[0, 2 π)$ : $- \frac{π}{2}$ Find the reference angle in radians $θ = \frac{19 π}{4}$ . Find the reference angle of $θ$ . What is the reference angle for an angle of $- \frac{25 π}{12}$ in standard position? Find the reference angle of $- \frac{22 π}{5}$ . $θ = - \frac{55 π}{12}$ . Find the reference angle of $θ$ . Find the reference angle of $\frac{35 π}{6}$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Coterminal and Reference Angles

Date Period

Answer each question.

Find a coterminal angle
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $960^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 750^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 690^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $945^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 1035^{\circ}$

Find the reference angle
What is the reference angle of $- 495^{\circ}$ ?
Find the reference angle of $435^{\circ}$ .
An angle of $1245^{\circ}$ is in standard position. Find its reference angle.
What is the reference angle of $770^{\circ}$ ?
Find the reference angle of $- 170^{\circ}$ .

Find a coterminal angle in radians
Find the coterminal angle in $[0, 2 π)$ : $\frac{19 π}{3}$
Find the coterminal angle in $[0, 2 π)$ : $- \frac{15 π}{2}$
Find the coterminal angle in $[0, 2 π)$ : $8 π$
Find the coterminal angle in $[0, 2 π)$ : $- 3 π$
Find the coterminal angle in $[0, 2 π)$ : $- \frac{π}{2}$

Find the reference angle in radians
$θ = \frac{19 π}{4}$ . Find the reference angle of $θ$ .
What is the reference angle for an angle of $- \frac{25 π}{12}$ in standard position?
Find the reference angle of $- \frac{22 π}{5}$ .
$θ = - \frac{55 π}{12}$ . Find the reference angle of $θ$ .
Find the reference angle of $\frac{35 π}{6}$ .



Sigma Prep · sigmaprep.io/worksheets Name Coterminal and Reference AnglesAnswer keyVersion 2 Date Period Answer each question. Find a coterminal angle Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $960^{\circ}$ $- 120^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 750^{\circ}$ $- 30^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 690^{\circ}$ $- 330^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $945^{\circ}$ $- 135^{\circ}$ Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 1035^{\circ}$ $- 315^{\circ}$ Find the reference angle What is the reference angle of $- 495^{\circ}$ ? $45^{\circ}$ Find the reference angle of $435^{\circ}$ . $75^{\circ}$ An angle of $1245^{\circ}$ is in standard position. Find its reference angle. $15^{\circ}$ What is the reference angle of $770^{\circ}$ ? $50^{\circ}$ Find the reference angle of $- 170^{\circ}$ . $10^{\circ}$ Find a coterminal angle in radians Find the coterminal angle in $[0, 2 π)$ : $\frac{19 π}{3}$ $\frac{π}{3}$ Find the coterminal angle in $[0, 2 π)$ : $- \frac{15 π}{2}$ $\frac{π}{2}$ Find the coterminal angle in $[0, 2 π)$ : $8 π$ $0$ Find the coterminal angle in $[0, 2 π)$ : $- 3 π$ $π$ Find the coterminal angle in $[0, 2 π)$ : $- \frac{π}{2}$ $\frac{3 π}{2}$ Find the reference angle in radians $θ = \frac{19 π}{4}$ . Find the reference angle of $θ$ . $\frac{π}{4}$ What is the reference angle for an angle of $- \frac{25 π}{12}$ in standard position? $\frac{π}{12}$ Find the reference angle of $- \frac{22 π}{5}$ . $\frac{2 π}{5}$ $θ = - \frac{55 π}{12}$ . Find the reference angle of $θ$ . $\frac{5 π}{12}$ Find the reference angle of $\frac{35 π}{6}$ . $\frac{π}{6}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Coterminal and Reference AnglesAnswer keyVersion 2

Date Period

Answer each question.

Find a coterminal angle
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $960^{\circ}$ $- 120^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 750^{\circ}$ $- 30^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 690^{\circ}$ $- 330^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $945^{\circ}$ $- 135^{\circ}$
Find the coterminal angle in $[- 360^{\circ}, 0^{\circ})$ : $- 1035^{\circ}$ $- 315^{\circ}$

Find the reference angle
What is the reference angle of $- 495^{\circ}$ ? $45^{\circ}$
Find the reference angle of $435^{\circ}$ . $75^{\circ}$
An angle of $1245^{\circ}$ is in standard position. Find its reference angle. $15^{\circ}$
What is the reference angle of $770^{\circ}$ ? $50^{\circ}$
Find the reference angle of $- 170^{\circ}$ . $10^{\circ}$

Find a coterminal angle in radians
Find the coterminal angle in $[0, 2 π)$ : $\frac{19 π}{3}$ $\frac{π}{3}$
Find the coterminal angle in $[0, 2 π)$ : $- \frac{15 π}{2}$ $\frac{π}{2}$
Find the coterminal angle in $[0, 2 π)$ : $8 π$ $0$
Find the coterminal angle in $[0, 2 π)$ : $- 3 π$ $π$
Find the coterminal angle in $[0, 2 π)$ : $- \frac{π}{2}$ $\frac{3 π}{2}$

Find the reference angle in radians
$θ = \frac{19 π}{4}$ . Find the reference angle of $θ$ . $\frac{π}{4}$
What is the reference angle for an angle of $- \frac{25 π}{12}$ in standard position? $\frac{π}{12}$
Find the reference angle of $- \frac{22 π}{5}$ . $\frac{2 π}{5}$
$θ = - \frac{55 π}{12}$ . Find the reference angle of $θ$ . $\frac{5 π}{12}$
Find the reference angle of $\frac{35 π}{6}$ . $\frac{π}{6}$

How to do these

Find the reference angle of $- \frac{11 π}{4}$

Add 4π, two full turns: -11π/4 + 16π/4 = 5π/4.
5π/4 is in Quadrant III.
Subtract π: 5π/4 - π = π/4.

The answer is $\frac{π}{4}$ .

Where students go wrong

Finding the reference angle before reducing. 1020° minus 180° is 840°, which is not between 0 and 90; take off whole turns first, 1020 - 720 = 300, and then 360 - 300 gives 60°.

Also called positive coterminal angle or finding reference angles.

What you can put on this worksheet

Coterminal angles: Find the coterminal angle in $[0^{\circ}, 360^{\circ})$ : $930^{\circ}$ → $210^{\circ}$
Reference angles: What is the reference angle of $235^{\circ}$ ? → $55^{\circ}$
Which quadrant an angle ends in: In which quadrant, or on which axis, does $187^{\circ}$ end? → Quadrant III
Sketch an angle in standard position: Sketch $190^{\circ}$ in standard position. Where does its terminal side lie? — axes for sketching an angle → Quadrant III
Coterminal angles in radians: Find the coterminal angle in $[0, 2 π)$ : $\frac{11 π}{3}$ → $\frac{5 π}{3}$
Reference angles in radians: Find the reference angle of $\frac{4 π}{3}$ . → $\frac{π}{3}$
Negative and radian angles, read from a drawing, coterminal or not: Find one positive and one negative coterminal angle:
$\frac{13 π}{12}$ → $\frac{37 π}{12}, - \frac{11 π}{12}$
Angles with a given reference angle: List four angles between $0^{\circ}$ and $720^{\circ}$ , one in each quadrant, with reference angle $20^{\circ}$ → For example:
$20^{\circ},$ $340^{\circ},$ $520^{\circ},$ $560^{\circ}$
The whole angle from a drawing, in radians: Find the measure of the angle, in radians. — an angle in standard position, labeled x, y, π/4 → $\frac{5 π}{4}$

Questions about these worksheets

Yes. Every coterminal and reference angles 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 coterminal and reference angles 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.

You pick from 9: coterminal angles, reference angles, which quadrant an angle ends in, sketch an angle in standard position, coterminal angles in radians, reference angles in radians, negative and radian angles, read from a drawing, coterminal or not, angles with a given reference angle and the whole angle from a drawing, in radians. Tick as many as you want and set how many of each, or let it spread them evenly.

Measuring the reference angle from the y-axis, or subtracting from 360 in the wrong quadrant. It is always to the nearest part of the x-axis, so the answer is always between 0 and 90.

Coterminal and reference angles worksheet for Precalculus

Select your difficulty

Find a coterminal angle

Find the reference angle

Find a coterminal angle in radians

Find the reference angle in radians

Find a coterminal angle

Find the reference angle

Find a coterminal angle in radians

Find the reference angle in radians

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these coterminal and reference angles worksheets free?+

Do the coterminal and reference angles worksheets come with an answer key?+

Are these coterminal and reference angles worksheets printable?+

What grade are these coterminal and reference angles worksheets for?+

Can I get a different version of the same coterminal and reference angles worksheet?+

Is this a free alternative to Kuta Software for coterminal and reference angles?+

Can I choose how hard the coterminal and reference angles questions are?+

What kinds of question are on a coterminal and reference angles worksheet?+

What do students get wrong with coterminal and reference angles?+