Characteristics of Sine / Cosine Graphs is a Grade 12 mathematics worksheet that builds students’ ability to interpret and compare trigonometric graphs. Across 17 items—including multiple-select, multiple-choice, and fill-in-the-blank questions—students identify amplitude, period, midline, domain, and range; recognize sine and cosine graphs; and read key features from displayed functions. Several items require students to determine values from a graph, while others reinforce the meaning of each characteristic and the relationship between maximum and minimum values.
This worksheet supports independent practice, guided instruction, or a focused review of sinusoidal graph characteristics. Students apply vocabulary such as amplitude and period, identify the equation of a graph’s midline, and distinguish the length of a cycle from the graph’s vertical range. It is a free printable worksheet with a complete answer key, making it useful for Grade 12 practice, checking understanding, and preparing students to analyze sine and cosine functions more confidently.
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Characteristics of Sine / Cosine graphs
Total questions: 17
Name
Class
Date
1.
Which choices below best describes this graph?
(May be more than 1 correct choice)
a)
b)
c)
Midline of y = -1
d)
Amplitude of 3 units
2.
The __________ represents half the distance between the max and min of a sine or cosine graph.
a)
Period
b)
Frequency
c)
Extreme Values
d)
Amplitude
3.
What is the domain and range of y=sinx?
a)
D: (-∞, ∞) R: [-1, 1]
b)
D: (-∞, ∞) R: [-π, π]
c)
D: (∞, -∞) R: [-1, 1]
d)
D: (-∞, ∞) R: [-∞, ∞]
4.
What is the amplitude of the graph?
a)
1
b)
2
c)
4
d)
-4
5.
What is the amplitude of this function?
a)
2
b)
2π
c)
-2
d)
1
6.
The period of a function is
a)
how long one cycle is before the function repeats
b)
how high and low the function goes from the center line
c)
the range of the function
7.
Which trig function is shown?
a)
sine
b)
cosine
c)
tangent
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.
Select the cosine graph.
a)
b)
c)
10.
What are the Amplitude, Period and Midline of this sin graph?
a)
Amp = 3 Period = 2π
Midline y = -1
b)
Amp = 3
Period = π
Midline y = 3
c)
Amp = 2 Period = 3π Midline y = 0
d)
Amp = 2 Period = 2π Midline y = 1
11.
What is the amplitude of the given graph?
(a)
12.
What is the period of the given graph?
a)
b)
c)
d)
13.
What is the EQUATION OF THE MIDLINE for the given graph?
(a)
14.
Which choice below represents the Domain and Range of the given graph?
a)
b)
c)
d)
15.
If the maximum and minimum values in a Sine graph are 18 units apart, what is the amplitude of the graph? (Just give the number)
(a)
16.
Which choice(s) below are NOT true about the parent functions for Sine (y = sin x) and Cosine (y = cos x)?
a)
They have the same max and min values
b)
They both have the same period
c)
They both have the same y-intercepts
d)
They both have the same midlines
e)
They both have the same amplitude
17.
Which given choice(s) have a period of 3Π/2 ?
a)
b)
c)
d)
Answer Key
Characteristics of Sine / Cosine graphs
Total questions: 17
1.
a) , d)
Amplitude of 3 units
2.
d) Amplitude
3.
a) D: (-∞, ∞) R: [-1, 1]
4.
a)
1
5.
a) 2
6.
a) how long one cycle is before the function repeats
7.
a)
sine
8.
a)
the length of one cycle
9.
b)
10.
d)
Amp = 2 Period = 2π Midline y = 1
11.
5
12.
c)
13.
y=3
14.
b)
15.
9
16.
c)
They both have the same y-intercepts
17.
b)
140 %
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FAQs
What does this sine and cosine graphs worksheet cover?
This Grade 12 worksheet gives students 17 mixed-format questions on interpreting sine and cosine graphs. Students identify amplitude, period, midline, domain, and range, distinguish sine from cosine graphs, and use graph features to determine values such as the midline equation and amplitude from the distance between maximum and minimum points.
How can I use this worksheet to teach amplitude, period, and midline?
Introduce the worksheet by having students define amplitude as half the distance between a graph’s maximum and minimum and period as the length of one repeating cycle. Then model one graph-reading item by locating its maximum, minimum, and center line before students work through the multiple-choice and fill-in-the-blank questions. Use the items asking students to identify a sine or cosine graph and determine domain and range as prompts for students to justify how the graph’s shape and values support their answers.
What mistakes should I watch for when students complete this worksheet?
Students may confuse amplitude with the full vertical distance from maximum to minimum, or confuse period with the graph’s range. Watch for students choosing a midline from an extreme value instead of the horizontal center between the maximum and minimum, reversing domain and range, or identifying sine and cosine from incomplete visual cues. In the fill-in-the-blank items, check that students give the requested numerical amplitude or write the midline as an equation such as y = a constant.
How do I assign and grade this sine and cosine graphs worksheet?
Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all included items. Assign the PDF for handwritten practice or use the digital quiz for online responses; printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support classrooms working to reduce screen time.
How can I differentiate this worksheet for my students?
Use the worksheet’s Advanced Settings to adjust font spacing and font size so graph-based multiple-choice items and fill-in-the-blank responses are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language, while keeping the amplitude, period, midline, domain, and range tasks intact.
Where can I find more free 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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
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