Worksheets · Precalculus

Graphing sine and cosine worksheet for Precalculus

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. Half the sheet runs the other way: read the amplitude, period and any shifts off a drawn graph and write its equation.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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 from 0 to 2π, or write the equation of each graph.

  1. Graph sine and cosine

    Graph y=sin⁡(2x)−1π/2π3π/22π−4−3−2−101234
  2. Graph y=2sin⁡(x)π/2π3π/22π−4−3−2−101234
  3. Graph y=3cos⁡(x)π/2π3π/22π−4−3−2−101234
  4. Graph y=3sin⁡(x)+2π/2π3π/22π−6−4−20246
  5. Graph y=2cos⁡(2x)−1π/2π3π/22π−4−3−2−101234
  6. Graph y=2cos⁡(x)+1π/2π3π/22π−4−3−2−101234
  7. Graph y=4sin⁡(2x)+1π/2π3π/22π−6−4−20246
  8. Graph y=4cos⁡(x)−1π/2π3π/22π−6−4−20246
  9. Graph y=3sin⁡(2x)π/2π3π/22π−4−3−2−101234
  10. Graph y=4cos⁡(2x)+2π/2π3π/22π−6−4−20246

  1. Write a trig equation from the graph

    Write a sine or cosine equation for the graph.π/2π3π/22π−6−4−20246
  2. Write an equation for the graph.π/2π3π/22π−4−3−2−101234
  3. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−6−4−20246
  4. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−4−3−2−101234
  5. Write a sine or cosine equation for the graph.π/2π3π/22π−6−4−20246
  6. Write an equation for the graph.π/2π3π/22π−4−3−2−101234
  7. Write a sine or cosine equation for the graph.π/2π3π/22π−4−3−2−101234
  8. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−4−2024
  9. Write an equation for the graph.π/2π3π/22π−4−2024
  10. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−4−3−2−101234

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 from 0 to 2π, or write the equation of each graph.

  1. Graph sine and cosine

    Graph y=sin⁡(2x)−1π/2π3π/22π−4−3−2−101234Amplitude 1, period π, down 1
  2. Graph y=2sin⁡(x)π/2π3π/22π−4−3−2−101234Amplitude 2, period 2π
  3. Graph y=3cos⁡(x)π/2π3π/22π−4−3−2−101234Amplitude 3, period 2π
  4. Graph y=3sin⁡(x)+2π/2π3π/22π−6−4−20246Amplitude 3, period 2π, up 2
  5. Graph y=2cos⁡(2x)−1π/2π3π/22π−4−3−2−101234Amplitude 2, period π, down 1
  6. Graph y=2cos⁡(x)+1π/2π3π/22π−4−3−2−101234Amplitude 2, period 2π, up 1
  7. Graph y=4sin⁡(2x)+1π/2π3π/22π−6−4−20246Amplitude 4, period π, up 1
  8. Graph y=4cos⁡(x)−1π/2π3π/22π−6−4−20246Amplitude 4, period 2π, down 1
  9. Graph y=3sin⁡(2x)π/2π3π/22π−4−3−2−101234Amplitude 3, period π
  10. Graph y=4cos⁡(2x)+2π/2π3π/22π−6−4−20246Amplitude 4, period π, up 2

  1. Write a trig equation from the graph

    Write a sine or cosine equation for the graph.π/2π3π/22π−6−4−20246Sample answer: y=4cos⁡(x)−1
  2. Write an equation for the graph.π/2π3π/22π−4−3−2−101234Sample answer: y=2sin⁡(2x)+1
  3. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−6−4−20246Sample answer: y=3cos⁡(2x)+2
  4. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−4−3−2−101234Sample answer: y=sin⁡(x)
  5. Write a sine or cosine equation for the graph.π/2π3π/22π−6−4−20246Sample answer: y=4cos⁡(x)−2
  6. Write an equation for the graph.π/2π3π/22π−4−3−2−101234Sample answer: y=3sin⁡(2x)
  7. Write a sine or cosine equation for the graph.π/2π3π/22π−4−3−2−101234Sample answer: y=sin⁡(x)−2
  8. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−4−2024Sample answer: y=2sin⁡(2x)+2
  9. Write an equation for the graph.π/2π3π/22π−4−2024Sample answer: y=3cos⁡(2x)+1
  10. Use the amplitude, period, phase shift and midline to write an equation for the graph.π/2π3π/22π−4−3−2−101234Sample answer: y=2cos⁡(2x)−1

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.

What you can put on this worksheet

Sine and cosine
Graph y=3sin⁡(2x) → Amplitude 3, period π
Write the equation from the graph
Write a sine or cosine equation for the graph. → Sample answer: y=3sin⁡(x)−1
Graph with a fraction in front of theta
Graph:
y=4sin⁡ ⁣(θ2) → Amplitude 4Period 4π

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.

You pick from 3: sine and cosine, write the equation from the graph and graph with a fraction in front of theta. Tick as many as you want and set how many of each, or let it spread them evenly.

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.