Precalculus coterminal and reference angles worksheet
Coterminal angles land in the same place, so add or subtract whole turns. A reference angle is the acute angle to the x-axis, which is what makes every trig value in any quadrant computable from the first one.
The reference angle is the distance to the x-axis.
210 minus 180.
The answer is 30∘.
Where students go wrong
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.
Also called positive coterminal angle or finding reference angles.
What you can put on this worksheet
Coterminal angles
Find a coterminal angle between 0∘ and 360∘:930∘→ 210∘
Reference angles
Find the reference angle: 140∘→ 40∘
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 2: coterminal angles and reference angles. 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.