Worksheets · Precalculus

Graphing sine and cosine worksheet

The number in front sets how tall the wave is and the number inside sets how often it repeats. The grid counts in quarters of pi, so the peaks and the zeros land on gridlines rather than between them.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Sine and Cosine

Date Period

Graph each function over one turn.

  1. Graph y=sin⁡(2(x−π))+1π/2π3π/22π42-2-40
  2. Graph y=−2cos⁡((x−π2))−1π/2π3π/22π42-2-40
  3. Graph y=cos⁡((x−π))−2π/2π3π/22π42-2-40
  4. Graph y=−sin⁡(x)+1π/2π3π/22π42-2-40
  5. Graph y=3sin⁡(2(x−π))−2π/2π3π/22π63-3-60
  6. Graph y=2cos⁡((x−π))−1π/2π3π/22π42-2-40
  7. Graph y=−2sin⁡((x−π))−1π/2π3π/22π42-2-40
  8. Graph y=−2sin⁡(2(x−π))−2π/2π3π/22π53-3-50
  9. Graph y=2sin⁡(2(x−π2))−2π/2π3π/22π53-3-50
  10. Graph y=sin⁡(2x)π/2π3π/22π42-2-40
  11. Graph y=3sin⁡(2x)−1π/2π3π/22π53-3-50
  12. Graph y=−2cos⁡(x)−1π/2π3π/22π42-2-40
  13. Graph y=cos⁡((x−π))π/2π3π/22π42-2-40
  14. Graph y=−cos⁡((x−π))−2π/2π3π/22π42-2-40
  15. Graph y=−2cos⁡((x−π))−1π/2π3π/22π42-2-40
  16. Graph y=−sin⁡(x)π/2π3π/22π42-2-40
  17. Graph y=2sin⁡(2(x−π))−1π/2π3π/22π42-2-40
  18. Graph y=−cos⁡(x)−1π/2π3π/22π42-2-40
  19. Graph y=3sin⁡(2(x−π2))+1π/2π3π/22π53-3-50
  20. Graph y=2cos⁡(2(x−π2))π/2π3π/22π42-2-40

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Sine and CosineAnswer keyVersion 1

Date Period

Graph each function over one turn.

  1. Graph y=sin⁡(2(x−π))+1π/2π3π/22π42-2-40Amplitude 1, period π, right π, up 1
  2. Graph y=−2cos⁡((x−π2))−1π/2π3π/22π42-2-40Amplitude 2, period 2π, right π2, down 1
  3. Graph y=cos⁡((x−π))−2π/2π3π/22π42-2-40Amplitude 1, period 2π, right π, down 2
  4. Graph y=−sin⁡(x)+1π/2π3π/22π42-2-40Amplitude 1, period 2π, up 1
  5. Graph y=3sin⁡(2(x−π))−2π/2π3π/22π63-3-60Amplitude 3, period π, right π, down 2
  6. Graph y=2cos⁡((x−π))−1π/2π3π/22π42-2-40Amplitude 2, period 2π, right π, down 1
  7. Graph y=−2sin⁡((x−π))−1π/2π3π/22π42-2-40Amplitude 2, period 2π, right π, down 1
  8. Graph y=−2sin⁡(2(x−π))−2π/2π3π/22π53-3-50Amplitude 2, period π, right π, down 2
  9. Graph y=2sin⁡(2(x−π2))−2π/2π3π/22π53-3-50Amplitude 2, period π, right π2, down 2
  10. Graph y=sin⁡(2x)π/2π3π/22π42-2-40Amplitude 1, period π
  11. Graph y=3sin⁡(2x)−1π/2π3π/22π53-3-50Amplitude 3, period π, down 1
  12. Graph y=−2cos⁡(x)−1π/2π3π/22π42-2-40Amplitude 2, period 2π, down 1
  13. Graph y=cos⁡((x−π))π/2π3π/22π42-2-40Amplitude 1, period 2π, right π
  14. Graph y=−cos⁡((x−π))−2π/2π3π/22π42-2-40Amplitude 1, period 2π, right π, down 2
  15. Graph y=−2cos⁡((x−π))−1π/2π3π/22π42-2-40Amplitude 2, period 2π, right π, down 1
  16. Graph y=−sin⁡(x)π/2π3π/22π42-2-40Amplitude 1, period 2π
  17. Graph y=2sin⁡(2(x−π))−1π/2π3π/22π42-2-40Amplitude 2, period π, right π, down 1
  18. Graph y=−cos⁡(x)−1π/2π3π/22π42-2-40Amplitude 1, period 2π, down 1
  19. Graph y=3sin⁡(2(x−π2))+1π/2π3π/22π53-3-50Amplitude 3, period π, right π2, up 1
  20. Graph y=2cos⁡(2(x−π2))π/2π3π/22π42-2-40Amplitude 2, period π, right π2

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

How to do these

Graph y=2sin⁡(2x)

  1. The 2 in front makes it reach 2 above and 2 below.
  2. The 2 inside halves the period, so one wave fits in pi instead of 2 pi.
  3. Mark the zeros, peaks and troughs at quarters of that period and join them.

The answer is Amplitude 2, period π.

Where students go wrong

Reading the number inside as the period itself. It divides into 2 pi rather than replacing it, so sin(2x) repeats every pi, not every 2. The other slip is starting a cosine at zero: it starts at its peak.

Also called sine graphs, cosine graphs, amplitude and period graphs or plotting sin and cos.

Questions about these worksheets

Yes. Every graphing sine and cosine 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 sine and cosine 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.

Reading the number inside as the period itself. It divides into 2 pi rather than replacing it, so sin(2x) repeats every pi, not every 2. The other slip is starting a cosine at zero: it starts at its peak.