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Sine and Cosine Graphs Worksheet

Explore the properties, transformations, and applications of sine and cosine graphs at a Grade 12 level, including amplitude, period, phase shift, and vertical shift.

Grade 12 Math TrigonometrySine and Cosine Graphs
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Includes

Multiple ChoiceFill in the Blanks3 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSF.TF.B.5CCSS.MATH.CONTENT.HSF.TF.C.8

Topics

TrigonometrySineCosineGraphsPre-Calculus
8 sections · Free to use · Printable
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Sine and Cosine Graphs

Name:

Date:

Score:

Read each question carefully and provide accurate answers. Show all your work for full credit.

1. What is the amplitude of the function y = 3sin(2x - π) + 1?

a

1

b

2

c

3

d

π

2. Which of the following represents the period of the function y = cos(x/3) - 2?

a

π/3

b

2π/3

c

3π

d

6π

3. The   of a sinusoidal function is half the distance between its maximum and minimum values.

4. A horizontal shift of a trigonometric graph is also known as a  .

5. Describe how the graph of y = -2sin(x + π/4) would be transformed from the parent function y = sin(x).

6. The range of the function y = 4cos(x) is [-4, 4].

T

True

F

False

7. A vertical shift of 3 units up for a sine graph changes its amplitude.

T

True

F

False

8. Graph one full period of the function y = 2cos(x - π/2). Label the amplitude, period, and phase shift.

-5-4-3-2-112345-5-4-3-2-112345

Amplitude:  

Period:  

Phase Shift:  

9. The depth of water at a certain dock varies with the tides. The depth varies from a minimum of 4 feet to a maximum of 10 feet. A full tidal cycle takes 12 hours. Write a sinusoidal function to model the depth of the water D (in feet) as a function of time t (in hours), assuming that at t=0, the depth is at its average.