AnswersTN-Algebra II B SC 26-27 For CreditEvaluating the Six Trigonometric Functions

Graphing Sine and Cosine Answers

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What is the range of y = sin(x)?

A
negative 1 less-than-or-equal-to y less-than-or-equal-to 1
Option A
B
Negative 2 pi less-than-or-equal-to y less-than-or-equal-to 2
Option B
C
Negative 0.5 less-than-or-equal-to y less-than-or-equal-to 0.5
Option C
26

Which of the functions is graphed?

A
y = –0.5cos(x) – 1
B
y = –0.5sin(x) + 1
C
y = 0.5sin(x) – 1
D
y = 0.5cos(x) + 1
27

Explain how the graph of y = –2sin(x) – 1 differs from the parent function. Make sure to compare key points used for graphing.

Answer:

The graph of y = –2sin(x) – 1 is the graph of the parent function stretched vertically by a factor of 2, reflected over the x-axis, and shifted 1 unit down. The maximum of the parent function is 1, the minimum is –1, and the amplitude is 1. The maximum of y = –2sin(x) – 1 is 1, the minimum is –3, and the amplitude is 2.

28

What is the range of y = 3sin(x)?

A
Option
B
Option
C
Option
29

Which did you include in your response?

A
The graph of y = –2sin(x) – 1 is the graph of the parent function stretched vertically by a factor of 2, reflected over the x-axis, and shifted 1 unit down.
B
The maximum of the parent function is 1, the minimum is –1, and the amplitude is 1.
C
The maximum of y = –2sin(x) – 1 is 1, the minimum is –3, and the amplitude is 2.
31

Maximum:

Answer:

4

32

What is the range of y = 3sin(x)?

A
negative 1 less-than-or-equal-to y less-than-or-equal-to 1
Option A
B
negative 3 less-than-or-equal-to y less-than-or-equal-to 3
Option B
C
negative one-third less-than-or-equal-to y less-than-or-equal-to one-third
Option C
34

Which did you include in your response?

A
The graph of y = –2sin(x) – 1 is the graph of the parent function stretched vertically by a factor of 2, reflected over the x-axis, and shifted 1 unit down.
B
The maximum of the parent function is 1, the minimum is –1, and the amplitude is 1.
C
The maximum of y = –2sin(x) – 1 is 1, the minimum is –3, and the amplitude is 2.
35

What is the range of y = –3sin(x)?

A
Option
B
Option
C
Option
36

Which function is graphed?

A
y = –2cos(x) – 4
B
y = 2cos(x) – 4
C
y = –2cos(x) + 4
D
y = 2cos(x) + 4
38

Amplitude:

Answer:

4

39

What is the range of y = –3sin(x)?

A
Negative 1 less-than-or-equal-to y less-than-or-equal-to 1
Option A
B
Negative 3 less-than-or-equal-to y less-than-or-equal-to 3
Option B
C
Negative one-third less-than-or-equal-to y less-than-or-equal-to one-third
Option C
40

Which function is graphed?

A
y = –2cos(x) – 4
B
y = 2cos(x) – 4
C
y = –2cos(x) + 4
D
y = 2cos(x) + 4

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