AnswersGA-Advanced Algebra Concepts and Connections CREvaluating the Six Trigonometric Functions

Graphing Sine and Cosine Answers

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1
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Complete the following statements for the cosine function shown in the graph.The minimum value is .

A
–1
B
–0.75
C
–0.5
D
–0.25
2
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The amplitude is .

A
0.25
B
0.5
C
0.75
D
1
3

The amplitude of the function shown in green is .

A
–6
B
–4
C
–3
D
3
E
4
F
6
4

An equation for this function is .

A
y = 0.75cos(x)
B
y = –0.75cos(x)
C
y = cos(0.75x)
D
y = cos(–0.75x)
5

Based on these results, changing the sign of a the maximum and minimum values of the graph of y = asin(x).

A
has no effect on
B
increases
C
decreases
6

The maximum value is .

A
0.25
B
0.5
C
0.75
D
1
7

The amplitude of the function shown in green is .

A
–6
B
–4
C
–3
D
3
E
4
F
6
8

The graph shows the function .

Question illustration
A
y = sin(x) + 6
B
y = cos(x) – 6
C
y = sin(x) – 6
D
y = cos(x) + 6
9

The function rule y = cos(x) + 2 describes graph shown here.

Question illustration
A
a
B
b
C
c
D
d
10

Identify the transformations needed to graph the cosine function y = –0.5cos(x) – 3 from the parent cosine function. Check all that apply.

A
vertical compression by a factor of 0.5
B
reflection across the y-axis
C
vertical translation 3 units down
D
vertical stretch by a factor of 0.5
E
reflection across the x-axis
F
vertical translation 3 units up
G
vertical translation 0.5 units down
11

Which of the following describe the sine function? Check all that apply.

A
Its range is all real numbers.
B
Its period is .
C
Its maximum is –1.
D
Its domain is all real numbers.
E
Its maximum is 1.
12

The domain is all real numbers for .

A
the sine function
B
the cosine function
C
both the sine and cosine function
13

Complete the following statements for the cosine function shown in the graph.The minimum value is –1✔ –0.75–0.5–0.25.

Answers:
.:–0.75
.:0.75
14

Use the graph to identify the amplitude for each function shown.The amplitude of the function shown in orange is .

A
–6
B
–4
C
–3
D
3
E
4
F
6
15

The graph shows the function .

Question illustration
A
y = sin(x) + 6
B
y = cos(x) – 6
C
y = sin(x) – 6
D
y = cos(x) + 6
16

Identify the transformations needed to graph the cosine function y = –0.5cos(x) – 3 from the parent cosine function. Check all that apply.

A
vertical compression by a factor of 0.5
B
reflection across the y-axis
C
vertical translation 3 units down
D
vertical stretch by a factor of 0.5
E
reflection across the x-axis
F
vertical translation 3 units up
G
vertical translation 0.5 units down
17

Question text not available

Answers:
.:–0.75
.:0.75
18

The function rule y = –0.5cos(x) – 3 describes graph X ab✔ cX d shown.

Question illustration
A
X a
B
b
C
✔ c
D
X d
19

The amplitude of the function shown in blue is .

A
–6
B
–4
C
–3
D
3
E
4
F
6
20

An x-intercept is for .

Question illustration
A
the sine function
B
the cosine function
C
both the sine and cosine function

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