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Writing Equations of Sine, Cosine, and Tangent Graphs - Printable Math Worksheets year 11 - Wayground

Writing Equations of Sine, Cosine, and Tangent Graphs

Annamaria Taylor

Created by Annamaria Taylor

15 questions

11th Grade

Math

Updated Sept 2026

Writing Equations of Sine, Cosine, and Tangent Graphs is a Grade 11 mathematics worksheet that helps students connect trigonometric graphs with their corresponding equations. Students analyze displayed sine, cosine, and tangent graphs and select the equation that represents each one, building fluency in interpreting graphical features and distinguishing among the three function families. The worksheet includes 15 questions: 13 multiple-choice items and 2 multiple-select items. The varied response formats require students to identify one correct equation in some cases and recognize all applicable choices in others, providing practice with both trigonometric graph interpretation and careful answer selection. This free printable worksheet includes a complete answer key for efficient review, independent practice, homework, or assessment preparation.

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WaygroundWorksheets

Writing Equations of Sine, Cosine, and Tangent Graphs

Total questions: 15

Name
Class
Date
1.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=12cos⁡2xy=\frac{1}{2}\cos2x

b)

y=12cos⁡xy=\frac{1}{2}\cos x

c)

y=−12cos⁡2xy=-\frac{1}{2}\cos2x

d)

y=−12cos⁡xy=-\frac{1}{2}\cos x

2.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=4sin⁡2xy=4\sin2x

b)

y=−4sin⁡2xy=-4\sin2x

c)

y=4sin⁡xy=4\sin x

d)

y=−4sin⁡xy=-4\sin x

3.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=4sin⁡4xy=4\sin4x

b)

y=−4sin⁡4xy=-4\sin4x

c)

y=4sin⁡2xy=4\sin2x

d)

y=−4sin⁡2xy=-4\sin2x

4.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=3cos⁡xy=3\cos x

b)

y=3sin⁡xy=3\sin x

c)

y=−3sin⁡xy=-3\sin x

d)

y=−3cos⁡xy=-3\cos x

5.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=2sin⁡4xy=2\sin4x

b)

y=−2sin⁡4xy=-2\sin4x

c)

y=2sin⁡(14x)y=2\sin\left(\frac{1}{4}x\right)

d)

y=−2sin⁡(14x)y=-2\sin\left(\frac{1}{4}x\right)

6.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=12cos⁡xy=\frac{1}{2}\cos x

b)

y=−12cos⁡xy=-\frac{1}{2}\cos x

c)

y=12sin⁡xy=\frac{1}{2}\sin x

d)

y=−12sin⁡xy=-\frac{1}{2}\sin x

7.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=3cos⁡4xy=3\cos4x

b)

y=−3cos⁡4xy=-3\cos4x

c)

y=3cos⁡2xy=3\cos2x

d)

y=−3cos⁡2xy=-3\cos2x

8.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=3cos⁡(13x)y=3\cos\left(\frac{1}{3}x\right)

b)

y=−3cos⁡(13x)y=-3\cos\left(\frac{1}{3}x\right)

c)

y=3cos⁡3xy=3\cos3x

d)

y=−3cos⁡3xy=-3\cos3x

9.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=12sin⁡(14x)y=\frac{1}{2}\sin\left(\frac{1}{4}x\right)

b)

y=−12sin⁡(14x)y=-\frac{1}{2}\sin\left(\frac{1}{4}x\right)

c)

y=12sin⁡4xy=\frac{1}{2}\sin4x

d)

y=−12sin⁡4xy=-\frac{1}{2}\sin4x

10.
What is the equation of the following graph?

What is the equation of the following graph?

a)

y=12cos⁡(14x)y=\frac{1}{2}\cos\left(\frac{1}{4}x\right)

b)

y=−12cos⁡(14x)y=-\frac{1}{2}\cos\left(\frac{1}{4}x\right)

c)

y=12sin⁡(14x)y=\frac{1}{2}\sin\left(\frac{1}{4}x\right)

d)

y=−12sin⁡(14x)y=-\frac{1}{2}\sin\left(\frac{1}{4}x\right)

11.
SELECT ALL THAT APPLY

SELECT ALL THAT APPLY

a)

y=tan⁡(π2x)+3y=\tan\left(\frac{\pi}{2}x\right)+3

b)

y=2tan⁡(π2x)+3y=2\tan\left(\frac{\pi}{2}x\right)+3

c)

y=tan⁡(12x)+3y=\tan\left(\frac{1}{2}x\right)+3

d)

y=5tan⁡(π2x)+3y=5\tan\left(\frac{\pi}{2}x\right)+3

12.
SELECT ALL THAT APPLY

SELECT ALL THAT APPLY

a)

y=tan⁡(4x)−1y=\tan\left(4x\right)-1

b)

y=6tan⁡(4x)−1y=6\tan\left(4x\right)-1

c)

y=tan⁡(14x)−1y=\tan\left(\frac{1}{4}x\right)-1

d)

y=3tan⁡(14x)−1y=3\tan\left(\frac{1}{4}x\right)-1

13.
Only select one answer.

Only select one answer.

a)

y=tan⁡(12x)y=\tan\left(\frac{1}{2}x\right)

b)

y=tan⁡2xy=\tan2x

c)

y=tan⁡2πxy=\tan2\pi x

d)

y=tan⁡(π2x)y=\tan\left(\frac{\pi}{2}x\right)

14.
Only select one answer.

Only select one answer.

a)

y=tan⁡(π3x)−3y=\tan\left(\frac{\pi}{3}x\right)-3

b)

y=tan⁡3x−3y=\tan3x-3

c)

y=tan⁡3πx−3y=\tan3\pi x-3

d)

y=tan⁡(13x)−3y=\tan\left(\frac{1}{3}x\right)-3

15.
Only select one answer.

Only select one answer.

a)

y=tan⁡(π3x)+7y=\tan\left(\frac{\pi}{3}x\right)+7

b)

y=tan⁡3x+7y=\tan3x+7

c)

y=tan⁡3πx+7y=\tan3\pi x+7

d)

y=tan⁡(13x)+7y=\tan\left(\frac{1}{3}x\right)+7

WaygroundAnswer Key

Writing Equations of Sine, Cosine, and Tangent Graphs

Total questions: 15

1.
a)

y=12cos⁡2xy=\frac{1}{2}\cos2x

2.
a)

y=4sin⁡2xy=4\sin2x

3.
a)

y=4sin⁡4xy=4\sin4x

4.
a)

y=3cos⁡xy=3\cos x

5.
a)

y=2sin⁡4xy=2\sin4x

6.
a)

y=12cos⁡xy=\frac{1}{2}\cos x

7.
a)

y=3cos⁡4xy=3\cos4x

8.
a)

y=3cos⁡(13x)y=3\cos\left(\frac{1}{3}x\right)

9.
a)

y=12sin⁡(14x)y=\frac{1}{2}\sin\left(\frac{1}{4}x\right)

10.
a)

y=12cos⁡(14x)y=\frac{1}{2}\cos\left(\frac{1}{4}x\right)

11.
a)

y=tan⁡(π2x)+3y=\tan\left(\frac{\pi}{2}x\right)+3

, b)

y=2tan⁡(π2x)+3y=2\tan\left(\frac{\pi}{2}x\right)+3

, d)

y=5tan⁡(π2x)+3y=5\tan\left(\frac{\pi}{2}x\right)+3

12.
a)

y=tan⁡(4x)−1y=\tan\left(4x\right)-1

, b)

y=6tan⁡(4x)−1y=6\tan\left(4x\right)-1

13.
a)

y=tan⁡(12x)y=\tan\left(\frac{1}{2}x\right)

14.
a)

y=tan⁡(π3x)−3y=\tan\left(\frac{\pi}{3}x\right)-3

15.
c)

y=tan⁡3πx+7y=\tan3\pi x+7

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FAQs

What does this worksheet cover?

This Grade 11 worksheet focuses on identifying the equations represented by displayed sine, cosine, and tangent graphs. Its 15 items—13 multiple choice and 2 multiple select—require students to connect each graph to its correct equation and distinguish when one or several answer choices apply.

How can I use this worksheet to teach students to write equations from trigonometric graphs?

Begin by reviewing how the visual form of a sine, cosine, or tangent graph corresponds to its equation, then model the reasoning process on one displayed graph. Have students explain why their selected equation matches the graph before completing the remaining multiple-choice and multiple-select items, using the answer key to discuss competing choices.

What mistakes should I watch for when students complete this worksheet?

Students may confuse sine, cosine, and tangent graphs when selecting an equation, or choose an equation without checking whether it matches the entire displayed graph. On the two multiple-select questions, also watch for students who identify one valid equation but overlook another, or select extra choices because they do not read the response direction carefully.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the displayed trigonometric graph questions and answer choices easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the sine, cosine, and tangent equation-matching tasks.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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