AnswersAZ-Common Core Algebra II BGraphing Sine and Cosine

Graphing Sine and Cosine Answers

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So, a is ✔ positivenegativezero.

A
✔ positive
B
negative
C
zero
3

The maximum value is and the

Answer:

1

4

minimum value is . So, the amplitude of

Answer:

-1

5

the function, |a|, is .

Answer:

1

6

The vertical translation is k = .

Answer:

0

7

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

Answer:

1

8

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

Answers:
, starting at the origin.:zero-max-zero-min-zero
.:positive
9

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
10

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

Answer:

-4

11

Identify which are zeroes of the function.

A
(0, 0)
B
Option
Option B
C
Option
Option C
12

Which graph has an amplitude of One-half ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
13

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
14

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

A
Option
Option A
B
Option
Option B
C
Option
Option C
15

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

A
Option
B
Option
C
Option
16

The amplitude of the graph is .

Answers:
The amplitude of the graph is:2
The midline is y =:4
17

Which function is graphed?

A
y = –2cos(x) – 4
B
y = 2cos(x) – 4
C
y = –2cos(x) + 4
D
y = 2cos(x) + 4
18

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
19

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).

20

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.

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