Worksheets · Precalculus

Cofunction identities worksheet for Precalculus

Precalculus uses the cofunction identities to rewrite a trig function of an angle as its cofunction of the complement. The pairs are sine with cosine, tangent with cotangent, and secant with cosecant, and the two angles always add to 90°, so cos 29° = sin 61°.

Also taught in Algebra 2 and Geometry, each 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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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Cofunction Identities

Date Period

Rewrite as a cofunction, or solve for the angle.

  1. Write cos⁡29∘ as a cofunction
  2. Write csc⁡57∘ as a cofunction
  3. Write sin⁡32∘ as a cofunction
  4. Write sec⁡11∘ as a cofunction
  5. Write cos⁡18∘ as a cofunction
  6. Write tan⁡76∘ as a cofunction
  7. Write sin⁡89∘ as a cofunction
  8. Write cot⁡67∘ as a cofunction
  9. Write sin⁡61∘ as a cofunction
  10. Write sec⁡38∘ as a cofunction
  11. Write cos⁡12∘ as a cofunction
  12. Write csc⁡20∘ as a cofunction
  13. Write cos⁡31∘ as a cofunction
  14. Write cot⁡9∘ as a cofunction
  15. Write sin⁡4∘ as a cofunction
  16. Write tan⁡48∘ as a cofunction
  17. Write cos⁡59∘ as a cofunction
  18. Write sec⁡41∘ as a cofunction
  19. Write sin⁡17∘ as a cofunction
  20. Write csc⁡70∘ as a cofunction

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

Sigma Prep · sigmaprep.io/worksheets

Name

Cofunction IdentitiesAnswer keyVersion 2

Date Period

Rewrite as a cofunction, or solve for the angle.

  1. Write cos⁡29∘ as a cofunctionsin⁡61∘
  2. Write csc⁡57∘ as a cofunctionsec⁡33∘
  3. Write sin⁡32∘ as a cofunctioncos⁡58∘
  4. Write sec⁡11∘ as a cofunctioncsc⁡79∘
  5. Write cos⁡18∘ as a cofunctionsin⁡72∘
  6. Write tan⁡76∘ as a cofunctioncot⁡14∘
  7. Write sin⁡89∘ as a cofunctioncos⁡1∘
  8. Write cot⁡67∘ as a cofunctiontan⁡23∘
  9. Write sin⁡61∘ as a cofunctioncos⁡29∘
  10. Write sec⁡38∘ as a cofunctioncsc⁡52∘
  11. Write cos⁡12∘ as a cofunctionsin⁡78∘
  12. Write csc⁡20∘ as a cofunctionsec⁡70∘
  13. Write cos⁡31∘ as a cofunctionsin⁡59∘
  14. Write cot⁡9∘ as a cofunctiontan⁡81∘
  15. Write sin⁡4∘ as a cofunctioncos⁡86∘
  16. Write tan⁡48∘ as a cofunctioncot⁡42∘
  17. Write cos⁡59∘ as a cofunctionsin⁡31∘
  18. Write sec⁡41∘ as a cofunctioncsc⁡49∘
  19. Write sin⁡17∘ as a cofunctioncos⁡73∘
  20. Write csc⁡70∘ as a cofunctionsec⁡20∘

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

How to do these

Write tan⁡38∘ as a cofunction

  1. The cofunction of tangent is cotangent.
  2. The complement of 38° is 90° - 38° = 52°.

The answer is cot⁡52∘.

Where students go wrong

Changing the function but not the angle. cos 29° is sin 61°, not sin 29°; the cofunction always takes the complement, 90° - 29°.

Also called cofunctions, complementary angle identities or sin cos complementary.

Questions about these worksheets

Yes. Every cofunction 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 cofunction 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 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.

Subtracting from 180 instead of 90. Cofunctions are about complementary angles; supplementary ones belong to a different identity.