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Precal Unit 7: Writing Sine and Cosine Functions From Graphs - Printable Math Worksheets 9th - 12th Grade - Wayground

Precal Unit 7: Writing Sine and Cosine Functions From Graphs

Keya Chakraborty

Created by Keya Chakraborty

10 questions

9th - 12th Grade

Math

Updated Mar 2026

Precal Unit 7: Writing Sine and Cosine Functions From Graphs is a free printable mathematics worksheet for students in Grades 9–12. This 10-question multiple-choice practice set focuses on reading key features of trigonometric graphs and using those features to identify or write functions. Students distinguish between the sine and cosine parent functions, determine amplitude, identify period, find vertical shift, and select equations that represent given graphs. The worksheet supports focused practice with the graph-to-equation process rather than broad trigonometry review. Students first interpret individual graph characteristics, then apply those observations when writing equations for sine and cosine functions. It can be used for independent practice, review, or a quick formative check of graph interpretation and function writing. The worksheet includes a complete answer key for efficient checking and feedback.

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Precal Unit 7: Writing Sine and Cosine Functions From Graphs

Total questions: 10

Name
Class
Date
1.
This is the parent function of:

This is the parent function of:

a)

Cosine

b)

Sine

c)

Linear

d)

Quadratic

2.
This is the parent function of:

This is the parent function of:

a)

Cosine

b)

Sine

c)

Linear

d)

Quadratic

3.
Find the amplitude for this graph.

Find the amplitude ∣A∣\left|A\right| for this graph.

a)

1

b)

2

c)

π\pi

d)

2π2\pi

4.
Find the amplitude for this graph.

Find the amplitude ∣A∣\left|A\right| for this graph.

a)

1

b)

2

c)

π\pi

d)

2π2\pi

5.
Find the period for this graph.

Find the period BB for this graph.

a)

1

b)

2

c)

π\pi

d)

2π2\pi

6.
Find the period for this graph.

Find the period BB for this graph.

a)

1

b)

2

c)

12\frac{1}{2}

d)

2π2\pi

7.
Find the vertical shift for this graph.

Find the vertical shift DD for this graph.

a)

0

b)

1

c)

2

d)

2π2\pi

8.
Find the vertical shift for this graph.

Find the vertical shift DD for this graph.

a)

-6

b)

-4

c)

-5

d)

0

9.
Write the equation for this graph.

Write the equation for this graph.

a)

f(x)=sin⁡(x)f\left(x\right)=\sin\left(x\right)

b)

f(x)=2sin⁡(x)f\left(x\right)=2\sin\left(x\right)

c)

f(x)=cos⁡(x)f\left(x\right)=\cos\left(x\right)

d)

f(x)=2cos⁡(x)f\left(x\right)=2\cos\left(x\right)

10.
Write the equation for this graph.

Write the equation for this graph.

a)

f(x)=cos⁡(x)−5f\left(x\right)=\cos\left(x\right)-5

b)

f(x)=12cos⁡(5x)f\left(x\right)=\frac{1}{2}\cos\left(5x\right)

c)

f(x)=cos⁡(x2)−4f\left(x\right)=\cos\left(\frac{x}{2}\right)-4

d)

f(x)=cos⁡(x2)−5f\left(x\right)=\cos\left(\frac{x}{2}\right)-5

WaygroundAnswer Key

Precal Unit 7: Writing Sine and Cosine Functions From Graphs

Total questions: 10

1.
a)

Cosine

2.
b)

Sine

3.
b)

2

4.
a)

1

5.
a)

1

6.
c)

12\frac{1}{2}

7.
a)

0

8.
c)

-5

9.
b)

f(x)=2sin⁡(x)f\left(x\right)=2\sin\left(x\right)

10.
d)

f(x)=cos⁡(x2)−5f\left(x\right)=\cos\left(\frac{x}{2}\right)-5

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FAQs

What does this worksheet cover?

This Grade 9–12 mathematics worksheet covers writing sine and cosine functions from graphs through 10 multiple-choice questions. Students identify sine and cosine parent functions, determine amplitude, period, and vertical shift, and use those features to select equations that match the graphs.

How can I use this worksheet to teach students to write sine and cosine functions from graphs?

Use the questions in sequence: first review how a graph reveals its sine or cosine parent function, then have students identify amplitude, period, and vertical shift before combining those features into an equation. Ask students to explain which graph feature supports each answer, especially when they move from the individual feature questions to the final equation-writing items.

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

Students may confuse the sine and cosine parent graphs, read the top or bottom of a graph as the amplitude instead of measuring from the midline, or mistake the graph’s horizontal cycle length for its period. When finding vertical shift, check that they use the graph’s midline rather than its maximum or minimum; in the equation questions, have them verify that all identified features appear in the selected function.

How do I assign and grade this worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key included for the amplitude, period, vertical-shift, parent-function, and equation items. For printable submissions, scan student work with the Wayground for Teachers app to streamline grading.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the graph-based multiple-choice items are easier to read and annotate. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the sine and cosine graph questions.

Where can I find more worksheets like this on Wayground?

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

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