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13.4-13.5 Sin and Cos Graphs - Printable Math Worksheets 9th - 12th Grade - Wayground

13.4-13.5 Sin and Cos Graphs

20 questions

9th - 12th Grade

Math

Updated Mar 2026

13.4-13.5 Sin and Cos Graphs is a Grade 9–12 mathematics worksheet with 20 multiple-choice questions focused on interpreting sine and cosine functions. Students identify equations from graphs, distinguish sine from cosine, determine amplitude and period, and recognize how coefficients affect a graph’s vertical stretch and horizontal cycle length. Items also include positive and negative coefficients, helping students connect the sign and coefficient structure of an equation to its graphical features. This free printable worksheet is useful for guided practice, independent review, homework, or a quick check of understanding after introducing trigonometric graphs. Students must read visual features such as starting behavior, amplitude, and repeat length, then select the equation or property that matches. An answer key is included so teachers can review misconceptions efficiently or support self-checking.

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13.4-13.5 Sin and Cos Graphs

Total questions: 20

Name
Class
Date
1.
This is the graph of...
This is the graph of...
a)
y = 3sin(4x)
b)
y = 4sin(3x)
c)
y = 3cos(4x)
d)
y = 4cos(3x)
2.
What is the period of y = 4Cos(2x)?
a)
4π
b)
π
c)
2π
d)
π/2
3.
This graph has a period of...
This graph has a period of...
a)
π/2
b)
π
c)
3π/2
d)
2π
4.
This is the graph of...
This is the graph of...
a)
y = -6sin(x)
b)
y = 6sin(x)
c)
y = -6cos(x)
d)
y = 6cos(x)
5.
This is the graph of...
This is the graph of...
a)
y = 2cos(5x)
b)
y = 2sin(5x)
c)
y = 5cos(2x)
d)
y = 5sin(2x)
6.
This is the graph of ...
This is the graph of ...
a)
y = -(1/2)sinx
b)
y = (1/2)sinx
c)
y = (1/2)cosx
d)
y = -(1/2)cosx
7.
What is the difference between y = sinx and y = 4sinx when graphed?
a)
a period change
b)
an amplitude change
c)
a phase shift
d)
no difference in graphs
8.
This is the graph of...
This is the graph of...
a)
y = 6 cosx
b)
y = 6 sinx
c)
y = cos(6x)
d)
y = sin(6x)
9.
The amplitude of y = 4Cos(2x) is...
a)
4
b)
2
c)
8
d)
1
10.
The amplitude of y = -8sin(3x) is...
a)
2
b)
-2
c)
8
d)
-8
11.
Sine or Cosine?
Sine or Cosine?
a)
y=sinx
b)
y=cosx
12.
Sine or Cosine?
Sine or Cosine?
a)
y=sinx
b)
y=cosx
13.

The period of both the sine and cosine function is

a)

2π2\pi

b)

π\pi

c)

π2\frac{\pi}{2}

d)

0

14.

What is the period of y= -3sinx

a)

π

b)

2π

c)

3π

d)

4π

15.
What is the period of y=4cos5x
a)
2π/5
b)
π
c)
5
d)
5π
16.
What is the amplitude of the graph?
What is the amplitude of the graph? 
a)
1
b)
3
c)
6
d)
9
17.
What is the period of y = 4Cos(2x)?
a)
4π
b)
π
c)
2π
d)
π/2
18.
Question Image
a)
A
b)
B
c)
C
d)
D
19.
Question Image
a)
A
b)
B
c)
C
d)
D
20.
Question Image
a)
A
b)
B
c)
C
d)
D
WaygroundAnswer Key

13.4-13.5 Sin and Cos Graphs

Total questions: 20

1.
c) y = 3cos(4x)
2.
b) π
3.
d) 2π
4.
c) y = -6cos(x)
5.
d) y = 5sin(2x)
6.
a) y = -(1/2)sinx
7.
b) an amplitude change
8.
b) y = 6 sinx
9.
a) 4
10.
c) 8
11.
b) y=cosx
12.
a) y=sinx
13.
a)

2π2\pi

14.
b)

2π

15.
a) 2π/5
16.
b) 3
17.
b) π
18.
c) C
19.
a) A
20.
d) D

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FAQs

What does the 13.4-13.5 Sin and Cos Graphs worksheet cover?

This worksheet uses 20 multiple-choice questions to build skill in matching sine and cosine equations to their graphs and identifying amplitude and period. Students also distinguish sine from cosine and interpret how coefficients such as 4 in 4sin(x), 5 in cos(5x), or a negative sign change a graph’s vertical scale, cycle length, or orientation.

How can I use this worksheet to teach amplitude and period in sine and cosine graphs?

Introduce the worksheet by comparing a basic sine or cosine graph with equations that change one coefficient at a time. Have students predict whether the change affects amplitude or period before completing the graph-identification items, then use the multiple-choice options to explain why an equation such as 4cos(2x) has amplitude 4 and period π. Finish by asking students to justify each selected equation using its starting behavior, height, and repeat length.

What mistakes should I watch for when students complete this sine and cosine graphs worksheet?

Watch for students reversing the roles of the coefficients: the coefficient outside the function controls amplitude, while the coefficient multiplying x changes the period. Students may also report a negative amplitude instead of using the absolute value, confuse sine and cosine from the graph’s starting point, or overlook the negative sign when matching an equation such as -6cos(x).

How do I assign and grade this worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 20 multiple-choice questions. For printable submissions, you can grade student work by scanning it with the Wayground for Teachers app. The PDF option can also support schools that are reducing screen time.

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

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the graph-identification choices and trigonometric notation are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when that better supports students reading the prompts and answer choices.

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 build essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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