Worksheets · Precalculus

Graphing tangent and cotangent worksheet

Tangent has no amplitude, because it runs off to infinity between one asymptote and the next. Draw the asymptotes first and the rest of the shape has nowhere else to go.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Tangent and Cotangent

Date Period

Graph each function over one turn.

  1. Graph y=tan⁡(2(x−π))+1π/2π3π/22π42-2-40
  2. Graph y=−cot⁡((x−π2))−1π/2π3π/22π42-2-40
  3. Graph y=cot⁡((x−π))−2π/2π3π/22π42-2-40
  4. Graph y=−tan⁡(x)+1π/2π3π/22π42-2-40
  5. Graph y=2tan⁡(2(x−π))−2π/2π3π/22π53-3-50
  6. Graph y=cot⁡((x−π))−1π/2π3π/22π42-2-40
  7. Graph y=−tan⁡((x−π))−1π/2π3π/22π42-2-40
  8. Graph y=−tan⁡(2(x−π))−2π/2π3π/22π42-2-40
  9. Graph y=tan⁡(2(x−π2))−2π/2π3π/22π42-2-40
  10. Graph y=tan⁡(2x)π/2π3π/22π42-2-40
  11. Graph y=2tan⁡(2x)−1π/2π3π/22π42-2-40
  12. Graph y=−cot⁡(x)−1π/2π3π/22π42-2-40
  13. Graph y=cot⁡((x−π))π/2π3π/22π42-2-40
  14. Graph y=−cot⁡((x−π))−2π/2π3π/22π42-2-40
  15. Graph y=−cot⁡((x−π))−1π/2π3π/22π42-2-40
  16. Graph y=−tan⁡(x)π/2π3π/22π42-2-40
  17. Graph y=tan⁡(2(x−π))−1π/2π3π/22π42-2-40
  18. Graph y=2tan⁡(2(x−π2))+1π/2π3π/22π42-2-40
  19. Graph y=cot⁡(2(x−π2))π/2π3π/22π42-2-40
  20. Graph y=2tan⁡((x−π2))π/2π3π/22π42-2-40

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Tangent and CotangentAnswer keyVersion 1

Date Period

Graph each function over one turn.

  1. Graph y=tan⁡(2(x−π))+1π/2π3π/22π42-2-40Period π2, asymptotes every π2, right π, up 1
  2. Graph y=−cot⁡((x−π2))−1π/2π3π/22π42-2-40Period π, asymptotes every π, right π2, down 1
  3. Graph y=cot⁡((x−π))−2π/2π3π/22π42-2-40Period π, asymptotes every π, right π, down 2
  4. Graph y=−tan⁡(x)+1π/2π3π/22π42-2-40Period π, asymptotes every π, up 1
  5. Graph y=2tan⁡(2(x−π))−2π/2π3π/22π53-3-50Period π2, asymptotes every π2, right π, down 2
  6. Graph y=cot⁡((x−π))−1π/2π3π/22π42-2-40Period π, asymptotes every π, right π, down 1
  7. Graph y=−tan⁡((x−π))−1π/2π3π/22π42-2-40Period π, asymptotes every π, right π, down 1
  8. Graph y=−tan⁡(2(x−π))−2π/2π3π/22π42-2-40Period π2, asymptotes every π2, right π, down 2
  9. Graph y=tan⁡(2(x−π2))−2π/2π3π/22π42-2-40Period π2, asymptotes every π2, right π2, down 2
  10. Graph y=tan⁡(2x)π/2π3π/22π42-2-40Period π2, asymptotes every π2
  11. Graph y=2tan⁡(2x)−1π/2π3π/22π42-2-40Period π2, asymptotes every π2, down 1
  12. Graph y=−cot⁡(x)−1π/2π3π/22π42-2-40Period π, asymptotes every π, down 1
  13. Graph y=cot⁡((x−π))π/2π3π/22π42-2-40Period π, asymptotes every π, right π
  14. Graph y=−cot⁡((x−π))−2π/2π3π/22π42-2-40Period π, asymptotes every π, right π, down 2
  15. Graph y=−cot⁡((x−π))−1π/2π3π/22π42-2-40Period π, asymptotes every π, right π, down 1
  16. Graph y=−tan⁡(x)π/2π3π/22π42-2-40Period π, asymptotes every π
  17. Graph y=tan⁡(2(x−π))−1π/2π3π/22π42-2-40Period π2, asymptotes every π2, right π, down 1
  18. Graph y=2tan⁡(2(x−π2))+1π/2π3π/22π42-2-40Period π2, asymptotes every π2, right π2, up 1
  19. Graph y=cot⁡(2(x−π2))π/2π3π/22π42-2-40Period π2, asymptotes every π2, right π2
  20. Graph y=2tan⁡((x−π2))π/2π3π/22π42-2-40Period π, asymptotes every π, right π2

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

How to do these

Graph y=tan⁡(2x)

  1. Tangent repeats every pi, so tan(2x) repeats every pi over 2.
  2. The asymptotes sit halfway through each period, a quarter of pi apart from the start.
  3. Between two asymptotes the curve climbs from far below to far above, through the middle.

The answer is Period π2, asymptotes every π2.

Where students go wrong

Giving tangent an amplitude. It has none: the number in front stretches it vertically but the curve still runs to infinity. The other slip is spacing the asymptotes by 2 pi over b, which is the sine period, not the tangent one.

Also called tangent graphs, cotangent graphs, asymptotes of tangent or plotting tan.

Questions about these worksheets

Yes. Every graphing tangent and cotangent 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 graphing tangent and cotangent 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.

Giving tangent an amplitude. It has none: the number in front stretches it vertically but the curve still runs to infinity. The other slip is spacing the asymptotes by 2 pi over b, which is the sine period, not the tangent one.