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Graphing Sine and Cosine Amp & Midline shifts only - Printable Math Worksheets 10th - 12th Grade - Wayground

Graphing Sine and Cosine Amp & Midline shifts only

Coach PHILIPS

Created by Coach PHILIPS

12 questions

10th - 12th Grade

Math

This Grade 10–12 mathematics worksheet focuses on identifying and interpreting sine and cosine graphs with amplitude and midline shifts. Students begin by distinguishing the standard graphs from their y-axis starting values, recognizing sine at y = 0 and cosine at y = 1, then identify graph representations and select equations that match shifted sinusoidal graphs. The 12-item set includes 11 multiple-choice questions and one open-ended spring-break prompt, making it useful for guided practice, review, or a quick check of graph-to-equation understanding. The beach-themed language gives students a memorable way to connect graph features with positions above and below the midline while they analyze the displayed curves. This free printable worksheet includes a complete answer key, helping teachers review students’ choices and address confusion between a graph’s amplitude, midline, and starting position. It is designed for secondary mathematics learners who are beginning to connect visual transformations of sine and cosine functions to their equations.

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Graphing Sine and Cosine Amp & Midline shifts only

Total questions: 12

Name
Class
Date
1.

In your "day at the beach" graphing sine and cosine:

Where does y=sin(x) start on the y-axis?

a)

In the "sand"

or

y=0

b)

On the "cliff"

or

y=1

c)

Who cares?! SPRING BREAK HERE I COME

d)

Don't pick me

2.

In your "day at the beach" graphing sine and cosine:

Where does y=cos(x) start on the y-axis?

a)

In the "sand"

or

y=0

b)

On the "cliff"

or

y=1

c)

Who cares?! SPRING BREAK HERE I COME

d)

Don't pick me

3.

In your "day at the beach" graphing sine and cosine:

What does the lowest point on the graph represent?

a)

Being "under water"

b)

Being eaten by sharks

c)

Baby Shark DOO DOO DOO DOO DOO DOO

d)
In your "day at the beach" graphing sine and cosine: What does the lowest point on the graph represent?
4.
Which of the following is the graph of y=\sin\left(x\right) y = sin ( x ) ? Hint: remember your day at the beach!

Which of the following is the graph of  y=\sin\left(x\right)  ?

Hint: remember your day at the beach!

a)

The blue graph

b)

The red graph

5.
Which of the following is a graph of y=\cos\left(x\right) y = cos ( x ) ? Hint: remember your day at the beach!

Which of the following is a graph of  y=\cos\left(x\right)  ?

Hint: remember your day at the beach!

a)

The Blue graph

b)

The Red graph

6.
Which of the following is the correct equation for the graph given?

Which of the following is the correct equation for the graph given?

a)

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

b)

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

c)

y=2cos⁡(x)y=2\cos\left(x\right)  

d)

y=2sin⁡(x)y=2\sin\left(x\right)  

7.
Which of the following is the correct equation for the graph?

Which of the following is the correct equation for the graph?

a)

y=2sin⁡(x)y=2\sin\left(x\right)  

b)

y=2cos⁡(x)y=2\cos\left(x\right)  

c)

y=sin⁡(x)+2y=\sin\left(x\right)+2  

d)

y=cos⁡(x)+2y=\cos\left(x\right)+2

8.
Which of the following is the correct equation of the graph?

Which of the following is the correct equation of the graph?

a)

y=2sin⁡(x)y=2\sin\left(x\right)  

b)

y=2cos⁡(x)y=2\cos\left(x\right)  

c)

y=−2sin⁡(x)y=-2\sin\left(x\right)  

d)

y=−2cos⁡(x)y=-2\cos\left(x\right)  

9.
Which of the following is the correct equation of the graph?

Which of the following is the correct equation of the graph?

a)

y=3sin⁡(x)−1y=3\sin\left(x\right)-1

b)

y=3cos⁡(x)−1y=3\cos\left(x\right)-1  

c)

y=−cos⁡(x)+3y=-\cos\left(x\right)+3  

d)

y=−sin⁡(x)−1y=-\sin\left(x\right)-1  

10.
Which of the following is the correct equation of the graph?

Which of the following is the correct equation of the graph?

a)

y=−2cos⁡(x)+2y=-2\cos\left(x\right)+2

b)

y=−2sin⁡(x)−2y=-2\sin\left(x\right)-2

c)

y=2cos⁡(x)+2y=2\cos\left(x\right)+2

d)

y=2sin⁡(x)+2y=2\sin\left(x\right)+2

11.
Which of the following is the correct equation of the graph?

Which of the following is the correct equation of the graph?

a)

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

b)

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

c)

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

d)

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

12.
What are your big plans for spring break?!

What are your big plans for spring break?!

4 lines
WaygroundAnswer Key

Graphing Sine and Cosine Amp & Midline shifts only

Total questions: 12

1.
a)

In the "sand"

or

y=0

2.
b)

On the "cliff"

or

y=1

3.
a)

Being "under water"

4.
a)

The blue graph

5.
b)

The Red graph

6.
a)

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

7.
d)

y=cos⁡(x)+2y=\cos\left(x\right)+2

8.
c)

y=−2sin⁡(x)y=-2\sin\left(x\right)  

9.
b)

y=3cos⁡(x)−1y=3\cos\left(x\right)-1  

10.
b)

y=−2sin⁡(x)−2y=-2\sin\left(x\right)-2

11.
c)

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

12.
n/a

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FAQs

What does this worksheet cover about sine and cosine graphs?

This worksheet helps Grade 10–12 students distinguish the standard sine and cosine starting points, identify sine and cosine graph shapes, and match graphs with equations involving amplitude and midline shifts. Its 11 multiple-choice questions require students to read key graph features and connect those features to the correct function, followed by one open-ended spring-break prompt.

How can I use this worksheet to teach amplitude and midline shifts?

Introduce the standard sine and cosine graphs first, asking students to identify where each begins on the y-axis and how the beach analogy represents positions above or below the midline. Then have students annotate the displayed graphs before choosing equations, explaining how the vertical center and distance from that center support each answer. Use the answer key to discuss why the other graph or equation choices do not match.

What mistakes should I watch for on this sine and cosine worksheet?

Students may reverse the standard starting points by placing sine at y = 1 or cosine at y = 0. When matching equations to graphs, watch for students who identify the amplitude correctly but overlook the midline shift, or who use the graph’s highest or lowest point without considering its center line. They may also confuse which colored graph represents sine or cosine.

How do I assign and grade this graphing worksheet?

You can assign this sine and cosine worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable version also gives schools an option for practicing graph interpretation with less screen time.

How can I differentiate this sine and cosine graphing worksheet for my students?

Under the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size so graph-identification prompts and equation choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet’s written directions and beach-themed prompts into another language while students work through the same sine, cosine, amplitude, and midline items.

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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