AnswersAZ-Common Core Algebra II BChanges in Period and Phase Shift of Sine and Cosine Functions

Changes in Period and Phase Shift of Sine and Cosine Functions Answers

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1
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Which situations can be modeled with a periodic function?

A
The height of a flag on one blade of a windmill
Option A
B
The height of a baseball after it has been hit
Option B
C
The height of a ball suspended from a spring
Option C
2
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The period is seconds.

Answer:

PENDING

3

seconds.

A
pi/2
B
pi
C
2pi
4

k =

Answer:

40

5

To the nearest thousandth, find the position of the pendulum when t = 4.25 sec. d = in.

Answer not available
6

b = pi/20✔ pi/10pi/5

A
pi/20
B
pi/10
C
pi/5
7

Choose the equation of the model.

A
Option
Option A
B
Option
Option B
C
Option
Option C
8

Graph the function using the graphing calculator. Find the least positive value of t at which the pendulum is in the center.t = sec To the nearest thousandth, find the position of the pendulum when t = 4.25 sec. d = in.

Answers:
Part 1:0.5
9

a =

Answer:

PENDING

10

a is the ✔ length of the bladeheight of the windmillnumber of rotations per minute.

A
length of the blade
B
height of the windmill
C
number of rotations per minute
11

Which periodic function, sine or cosine, would be a simpler model for the situation? Explain.

Answer:

A cosine function would be a simpler model for the situation. Since the low tide (minimum depth) occurs at t = 0, a reflected cosine function can be used to model the data without needing a phase shift. Conversely, a sine function would require a phase shift to account for the starting position at the minimum.

12

This amplitude is meters. a = ⇒ -1.5

Answer:

1.5

13

Question text not available

Answer not available
14

The graph of these points follows a path resembling a .

A
cosine curve reflected across the y-axis
B
sine curve reflected across the y-axis
C
cosine curve reflected across the x-axis
D
sine curve reflected across the x-axis
15

Use the graph to write an equation y = acos[b(x – h)] + k to model the situation.The amplitude is , so a = . The period is , so b = .

Question illustration
Answers:
Part 1:30
Part 2:-30
16

The blades of the windmill turn on an axis that is feet from the ground.

A
5
B
15
C
20
D
25
17

Question text not available

Answer not available
18

The vertical shift, k, is the length of the blade✔ height of the windmillnumber of rotations per minute.

A
length of the blade
B
height of the windmill
C
number of rotations per minute
19

Which did you include in your response

A
A cosine function would be a simpler model for the situation.
B
The minimum depth (low tide) occurs at t = 0. A reflection of the cosine curve also has a minimum at t = 0.
C
A sine model would require a phase shift, while a cosine model does not.
20

Question text not available

Answer:

1.5

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