Worksheets · Precalculus

Precalculus double angle identities worksheet

Given the sine and cosine of an angle, the doubled angle follows from two short formulas. Every answer here is an exact fraction.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Double Angle Identities

Date Period

Evaluate each.

  1. If sin⁡θ=2853 and cos⁡θ=4553, find tan⁡2θ
  2. If sin⁡θ=3537 and cos⁡θ=1237, find tan⁡2θ
  3. If sin⁡θ=4873 and cos⁡θ=5573, find tan⁡2θ
  4. If sin⁡θ=4553 and cos⁡θ=2853, find tan⁡2θ
  5. If sin⁡θ=4041 and cos⁡θ=941, find tan⁡2θ
  6. If sin⁡θ=941 and cos⁡θ=4041, find tan⁡2θ
  7. If sin⁡θ=513 and cos⁡θ=1213, find tan⁡2θ
  8. If sin⁡θ=817 and cos⁡θ=1517, find tan⁡2θ
  9. If sin⁡θ=2129 and cos⁡θ=2029, find tan⁡2θ
  10. If sin⁡θ=725 and cos⁡θ=2425, find tan⁡2θ
  11. If sin⁡θ=35 and cos⁡θ=45, find tan⁡2θ
  12. If sin⁡θ=1665 and cos⁡θ=6365, find tan⁡2θ
  13. If sin⁡θ=1161 and cos⁡θ=6061, find tan⁡2θ
  14. If sin⁡θ=6365 and cos⁡θ=1665, find tan⁡2θ
  15. If sin⁡θ=1517 and cos⁡θ=817, find tan⁡2θ
  16. If sin⁡θ=2029 and cos⁡θ=2129, find tan⁡2θ
  17. If sin⁡θ=1213 and cos⁡θ=513, find tan⁡2θ
  18. If sin⁡θ=1237 and cos⁡θ=3537, find tan⁡2θ
  19. If sin⁡θ=2425 and cos⁡θ=725, find tan⁡2θ
  20. If sin⁡θ=5573 and cos⁡θ=4873, find tan⁡2θ

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Double Angle IdentitiesAnswer keyVersion 1

Date Period

Evaluate each.

  1. If sin⁡θ=2853 and cos⁡θ=4553, find tan⁡2θ25201241
  2. If sin⁡θ=3537 and cos⁡θ=1237, find tan⁡2θ−8401081
  3. If sin⁡θ=4873 and cos⁡θ=5573, find tan⁡2θ5280721
  4. If sin⁡θ=4553 and cos⁡θ=2853, find tan⁡2θ−25201241
  5. If sin⁡θ=4041 and cos⁡θ=941, find tan⁡2θ−7201519
  6. If sin⁡θ=941 and cos⁡θ=4041, find tan⁡2θ7201519
  7. If sin⁡θ=513 and cos⁡θ=1213, find tan⁡2θ120119
  8. If sin⁡θ=817 and cos⁡θ=1517, find tan⁡2θ240161
  9. If sin⁡θ=2129 and cos⁡θ=2029, find tan⁡2θ−84041
  10. If sin⁡θ=725 and cos⁡θ=2425, find tan⁡2θ336527
  11. If sin⁡θ=35 and cos⁡θ=45, find tan⁡2θ247
  12. If sin⁡θ=1665 and cos⁡θ=6365, find tan⁡2θ20163713
  13. If sin⁡θ=1161 and cos⁡θ=6061, find tan⁡2θ13203479
  14. If sin⁡θ=6365 and cos⁡θ=1665, find tan⁡2θ−20163713
  15. If sin⁡θ=1517 and cos⁡θ=817, find tan⁡2θ−240161
  16. If sin⁡θ=2029 and cos⁡θ=2129, find tan⁡2θ84041
  17. If sin⁡θ=1213 and cos⁡θ=513, find tan⁡2θ−120119
  18. If sin⁡θ=1237 and cos⁡θ=3537, find tan⁡2θ8401081
  19. If sin⁡θ=2425 and cos⁡θ=725, find tan⁡2θ−336527
  20. If sin⁡θ=5573 and cos⁡θ=4873, find tan⁡2θ−5280721

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

If sin⁡θ=35 and cos⁡θ=45, find sin⁡2θ

  1. sin of double the angle is 2 sin cos.
  2. 2 times 3 fifths times 4 fifths.

The answer is 2425.

Where students go wrong

Doubling the ratio instead of the angle. sin 2θ is not 2 sin θ, and the gap is large: with sin θ = 3/5 the two give 24/25 and 6/5, and the second is not even possible.

Also called double angle formulas, sin 2 theta or cos 2 theta.

Questions about these worksheets

Yes. Every double angle identities 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 double angle identities 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.

Doubling the ratio instead of the angle. sin 2θ is not 2 sin θ, and the gap is large: with sin θ = 3/5 the two give 24/25 and 6/5, and the second is not even possible.