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Graphing Sin and Cos - Printable Math Worksheets 12th Grade - Wayground

Graphing Sin and Cos

Brandon Humbert

Created by Brandon Humbert

16 questions

12th Grade

Math

Updated Oct 2026

Graphing Sin and Cos is a free printable Grade 12 mathematics worksheet with 16 multiple-choice questions on interpreting sine and cosine graphs. Students identify the period as the length of one cycle, use the period formula 2π/B, determine amplitudes, recognize where a cosine graph begins, and select equations that match graphs such as y = 2 sin θ and y = 5 cos x. The question set reinforces how coefficients affect the key features of trigonometric graphs. By comparing answer choices that vary in amplitude, function type, or input coefficient, students practise distinguishing vertical changes from horizontal changes and applying standard sine and cosine relationships. Use it for guided practice, independent review, or a quick check of Grade 12 graphing skills. The worksheet is available as a free printable PDF and includes an answer key for efficient checking.

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Graphing Sin and Cos

Total questions: 16

Name
Class
Date
1.
Question Image
a)

period: 6πperiod:\ 6\pi

b)

period: 3πperiod:\ 3\pi

c)

period: 2πperiod:\ 2\pi

d)

period: 8πperiod:\ 8\pi

2.
Question Image

a)

period: πperiod:\ \pi

b)

period: 2πperiod:\ 2\pi

c)

period: 3πperiod:\ 3\pi

d)

period: 4πperiod:\ 4\pi

3.
Question Image

a)

amp: 1amp:\ 1

b)

amp: 2amp:\ 2

c)

amp: 12amp:\ \frac{1}{2}

d)

amp: 0amp:\ 0

4.
Question Image

a)

amp: 4amp:\ 4

b)

amp: 2amp:\ 2

c)

amp: 1amp:\ 1

d)

amp: 0amp:\ 0

5.
Question Image

a)

sine function

b)

cosine function

6.
Question Image

a)

sine function

b)

cosine function

7.

What is the period of  y=4cos⁡5θy=4\cos5\theta  ? 

a)

2π/5

b)

π

c)

5

d)

5π

8.

The period of a function is

a)

the length of one cycle

b)

how high and low the function goes from the center line

c)

the range of the function

9.
What is the equation of the graph?

What is the equation of the graph?

a)

y = 2 cos θ

b)

y = sin θ

c)

y = 2 sin θ

d)

y = sin 2θ

10.

Where does the graph of cosine begin?

a)

(0, 0)

b)

(0, a)

c)

(0, π)\left(0,\ \pi\right)

d)

(1, π)\left(1,\ \pi\right)

11.
The period of a sine or cosine graph can be found by ....
a)
It's always 2π
b)
2π/B
c)
B(2π)
d)
2π+B
12.
10. What is the equation of the graph?
10.  What is the equation of the graph?
a)
 y = 2 cos x
b)
y = sin x
c)
y = 2 sin x
d)
y = sin 2x 
13.
11. What is the equation of graph?
11.  What is the equation of graph? 
a)
y = sin 5x
b)
y =  cos 5x
c)
y = 5 sin x
d)
y = 5 cos x 
14.
14. What is the amplitude of the graph?
14.  What is the amplitude of the graph? 
a)
1
b)
3
c)
6
d)
9
15.
What is the period of either graph? y = sin(x) & y = cos (x)
What is the period of either graph? 
y = sin(x)      &   y = cos (x)
a)
Pi
b)
2Pi
c)
Pi/2
d)
Pi/4 
16.
What is the period of the graph?
What is the period of the graph? 
a)
2Pi
b)
Pi
c)
Pi/2
d)
Pi/4 
WaygroundAnswer Key

Graphing Sin and Cos

Total questions: 16

1.
a)

period: 6πperiod:\ 6\pi

2.
d)

period: 4πperiod:\ 4\pi

3.
a)

amp: 1amp:\ 1

4.
a)

amp: 4amp:\ 4

5.
b)

cosine function

6.
a)

sine function

7.
a)

2π/5

8.
a)

the length of one cycle

9.
c)

y = 2 sin θ

10.
b)

(0, a)

11.
b) 2π/B
12.
c) y = 2 sin x
13.
d) y = 5 cos x 
14.
b) 3
15.
b) 2Pi
16.
b) Pi

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FAQs

What does the Graphing Sin and Cos worksheet cover?

This Grade 12 worksheet uses 16 multiple-choice questions to assess sine and cosine graph interpretation. Students identify amplitude, determine period using 2π/B, define period as the length of one cycle, recognize cosine’s starting point, and match equations such as y = 2 sin θ or y = 5 cos x to graphs.

How can I use this worksheet to teach sine and cosine graph features?

Introduce amplitude, period, and the standard starting behavior of sine and cosine before assigning the questions. Work through one equation-matching item as a class, asking students whether a coefficient changes the graph’s height or its cycle length, then have students justify their choices for the period and amplitude questions using 2π/B.

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

Students may confuse amplitude with period, treating the coefficient inside the input as a vertical change instead of using it in 2π/B. They may also select the wrong equation when sine and cosine are paired with different coefficients, or incorrectly identify the cosine graph’s starting point as (0, 0) rather than (0, a).

How do I assign and grade this sine and cosine worksheet?

Wayground provides Graphing Sin and Cos as a printable PDF and as a digital quiz, and the worksheet includes a complete answer key. For printable submissions, you can scan student work with the Wayground for Teachers app to grade it efficiently.

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

Because this worksheet presents graphing concepts in multiple-choice format, you can adjust font spacing and font size to make the equations, symbols, and answer choices easier to read. Under Advanced Settings, you can also enable a dyslexia-friendly font or translate the worksheet into another language.

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

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