Answers Algebra 2 MP 234 CHSGraphing Sine and Cosine

Graphing Sine and Cosine Answers

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Answers:

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Complete the following to analyze the graph shown.The graph follows the pattern for the sine function: max-zero-min-zero-maxzero-max-zero-min-zerozero-min-zero-max-zeromin, zero, max, zero, min, starting at the origin.

max-zero-min-zero-max

zero-max-zero-min-zero

zero-min-zero-max-zero

min, zero, max, zero, min

Which graph shows a periodic function with an amplitude of 2?

Option

Identify the maximum, minimum, and amplitude from the graph shown.Minimum:

Answer:

-4

Identify which are zeroes of the function.

(0, 0)

Option

Which graph has an amplitude of One-half ?

Option

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

Option

Which is the graph of y = 3sin(x) – 1?

Option

Which is the graph of y = –cos(x) – 2?

Option

The amplitude of the graph is .

Answer:

Which function is graphed?

y = –2cos(x) – 4

y = 2cos(x) – 4

y = –2cos(x) + 4

y = 2cos(x) + 4

Which of the functions is graphed?

y = –0.5cos(x) – 1

y = –0.5sin(x) + 1

y = 0.5sin(x) – 1

y = 0.5cos(x) + 1

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 is vertically stretched by a factor of 2, reflected over the x-axis, and shifted 1 unit down. The parent function has maximum 1, minimum −1, and amplitude 1, while the transformed graph has maximum 1, minimum −3, and amplitude 2. Its key points change from (0, 0), (π/2, 1), (π, 0), (3π/2, −1), (2π, 0) to (0, −1), (π/2, −3), (π, −1), (3π/2, 1), (2π, −1).

Which did you include in your response?

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.

. So, the amplitude of

Answers:

Selection 1:zero-max-zero-min-zero

Selection 2:positive

Which graph shows a periodic function with an amplitude of 2?

Answer not available

Identify the maximum, minimum, and amplitude from the graph shown.Minimum: Maximum: Amplitude:

Answers:

Part 1:-4

Part 2:4

Part 3:4

Question text not available

Answer not available

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

negative 1 less-than-or-equal-to y less-than-or-equal-to 1

Negative 2 pi less-than-or-equal-to y less-than-or-equal-to 2

Negative 0.5 less-than-or-equal-to y less-than-or-equal-to 0.5

Which is the graph of y = 3sin(x) – 1?

On a coordinate plane, a sine curve has a maximum of 2 and a minimum of negative 4. It crosses the y-axis at negative 2.

On a coordinate plane, a sine curve has a maximum of 4 and a minimum of negative 2. It crosses the y-axis at 1.

On a coordinate plane, a sine curve has a maximum of 0 and a minimum of negative 4. It crosses the y-axis at negative 2.

Question text not available

Answer not available

The amplitude of the graph is . The midline is y = .

Answer not available

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Answer not available

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Answer not available

So, a is positivenegativezero.

positive

negative

zero

Maximum:

Answer:

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

Option

The midline is y = .

Answer:

. So, the amplitude of

Answer not available

Question text not available

Answer not available

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

negative 1 less-than-or-equal-to y less-than-or-equal-to 1

negative 3 less-than-or-equal-to y less-than-or-equal-to 3

negative one-third less-than-or-equal-to y less-than-or-equal-to one-third

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Answer not available

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The maximum value is and the

Answer:

Amplitude:

Answer:

What is the range of y = –3sin(x)?

Option

. So, the amplitude of

Answer not available

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Answer not available

What is the range of y = –3sin(x)?

Negative 1 less-than-or-equal-to y less-than-or-equal-to 1

Negative 3 less-than-or-equal-to y less-than-or-equal-to 3

Negative one-third less-than-or-equal-to y less-than-or-equal-to one-third

Question text not available

Answer not available

minimum value is . So, the amplitude of

Answer:

-1

What is the range of y = –3sin(x) – 2?

Option

. So, the amplitude of

Answer not available

Question text not available

Answer not available

What is the range of y = –3sin(x) – 2?

Negative 1 less-than-or-equal-to y less-than-or-equal-to 1

Negative 3 less-than-or-equal-to y less-than-or-equal-to 3

Negative 5 less-than-or-equal-to y less-than-or-equal-to 5

the function, |a|, is .

Answer:

. So, the amplitude of

Answer not available

The vertical translation is k = .

Answer:

. So, the amplitude of

Answer not available

This is the graph of y = sin(x).

Answer:

This is the graph of y = sin(x).

Answer:

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Graphing Sine and Cosine Answers

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max-zero-min-zero-max

zero-max-zero-min-zero

zero-min-zero-max-zero

min, zero, max, zero, min

Which graph shows a periodic function with an amplitude of 2?

Option

Identify the maximum, minimum, and amplitude from the graph shown.Minimum:

Answer:

-4

Identify which are zeroes of the function.

(0, 0)

Option

Which graph has an amplitude of One-half ?

Option

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

Option

Which is the graph of y = 3sin(x) – 1?

Option

Which is the graph of y = –cos(x) – 2?

Option

The amplitude of the graph is .

Answer:

Which function is graphed?

y = –2cos(x) – 4

y = 2cos(x) – 4

y = –2cos(x) + 4

y = 2cos(x) + 4

Which of the functions is graphed?

y = –0.5cos(x) – 1

y = –0.5sin(x) + 1

y = 0.5sin(x) – 1

y = 0.5cos(x) + 1

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

Answer:

Which did you include in your response?

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.

. So, the amplitude of

Answers:

Selection 1:zero-max-zero-min-zero

Selection 2:positive

Which graph shows a periodic function with an amplitude of 2?

Answer not available

Identify the maximum, minimum, and amplitude from the graph shown.Minimum: Maximum: Amplitude:

Answers:

Part 1:-4

Part 2:4

Part 3:4

Question text not available

Answer not available

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

negative 1 less-than-or-equal-to y less-than-or-equal-to 1

Negative 2 pi less-than-or-equal-to y less-than-or-equal-to 2

Negative 0.5 less-than-or-equal-to y less-than-or-equal-to 0.5

Which is the graph of y = 3sin(x) – 1?

On a coordinate plane, a sine curve has a maximum of 2 and a minimum of negative 4. It crosses the y-axis at negative 2.

On a coordinate plane, a sine curve has a maximum of 4 and a minimum of negative 2. It crosses the y-axis at 1.

On a coordinate plane, a sine curve has a maximum of 0 and a minimum of negative 4. It crosses the y-axis at negative 2.

Question text not available

Answer not available

The amplitude of the graph is . The midline is y = .

Answer not available

Question text not available

Answer not available

Question text not available

Answer not available

So, a is positivenegativezero.

positive

negative

zero

Maximum:

Answer:

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

Option

The midline is y = .

Answer:

. So, the amplitude of

Answer not available

Question text not available

Answer not available

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

negative 1 less-than-or-equal-to y less-than-or-equal-to 1

negative 3 less-than-or-equal-to y less-than-or-equal-to 3

negative one-third less-than-or-equal-to y less-than-or-equal-to one-third

Question text not available

Answer not available

Question text not available

Answer not available

The maximum value is and the

Answer:

Amplitude:

Answer:

What is the range of y = –3sin(x)?

Option

. So, the amplitude of

Answer not available

Question text not available

Answer not available

What is the range of y = –3sin(x)?

Negative 1 less-than-or-equal-to y less-than-or-equal-to 1

Negative 3 less-than-or-equal-to y less-than-or-equal-to 3

Negative one-third less-than-or-equal-to y less-than-or-equal-to one-third

Question text not available

Answer not available

minimum value is . So, the amplitude of

Answer:

-1

What is the range of y = –3sin(x) – 2?

Option

. So, the amplitude of

Answer not available

Question text not available

Answer not available

What is the range of y = –3sin(x) – 2?

Negative 1 less-than-or-equal-to y less-than-or-equal-to 1

Negative 3 less-than-or-equal-to y less-than-or-equal-to 3

Negative 5 less-than-or-equal-to y less-than-or-equal-to 5

the function, |a|, is .

Answer:

. So, the amplitude of

Answer not available

The vertical translation is k = .

Answer:

. So, the amplitude of

Answer not available

This is the graph of y = sin(x).

Answer:

This is the graph of y = sin(x).

Answer:

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Graphing Sine and Cosine Answers

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Graphing Sine and Cosine Answers

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