AnswersAZ-Common Core Algebra II BGraphing Sine and Cosine

Graphing Sine and Cosine Answers

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Find the following (take ground level to be 0):Gum’s minimum height: ft

Answer:

6

22
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a = ,

Answers:
Part 2:7
Part 3:8
Part 4:7
Part 5:6
23

Graph the following points on the graphing calculator:Explain how to use the graph to write an equation to model the gum’s height. Be sure to identify the pattern of the points in your explanation, and identify the values of a and k.

Question illustration
Answer:

The pattern is min-zero-max-zero-min, which is the pattern for a cosine function of the form y = acos(x) + k, but is reflected over the x-axis (so a < 0). The amplitude is |a|, so a = –1 and |a| = 1. The midline is exactly between the max and the min, y = (6 + 8)/2 = 7, so k = 7. The equation is y = –cos(x) + 7.

24

b = ,

Question illustration
A
1 / 2
B
1
C
3 / 2
D
2
25

This is the pattern for a function.

A
sine
B
cosine
C
reflection of a sine
D
reflection of a cosine
26

When the boat has traveled 10 meters, the height of the barnacle is approximately:

A
–1 m
B
–0.544 m
C
0.544 m
D
1 m
27

Gum’s maximum height: ft

Answer:

8

28

b = ,

Answer:

7

29

The minimum height reached by the barnacleis m.

Answer:

-1

30

b = ,

Question illustration
Answer not available
31

This is the pattern for a function.

A
sine
B
cosine
C
reflection of a sine
D
reflection of a cosine
32

Question text not available

Answer not available
33

Check each of the following that you included in your explanation.

A
When the graph is below the x-axis, the barnacle is underwater.
B
The graph dips below the x-axis three times between x = 0 and x = 20, so the barnacle goes underwater three times.
C
Every time the barnacle goes underwater, the boat travels meters (one half the circumference of the wheel) before the barnacle comes back up, so the barnacle covers 3 meters underwater between x = 0 and x = 20.
Option C
34

Gum’s maximum height: ft

Answer not available
35

b = ,

Answer not available
36

Check all that you included in your answer.

A
The pattern is min-zero-max-zero-min, which is the pattern for a cosine function of the form y = acos(x) + k, but is reflected over the x-axis (so a < 0).
B
The amplitude is |a|, so a = –1 and |a| = 1.
C
The midline is exactly between the max and the min, y = (6 + 8)/2 = 7, so k = 7.
D
The equation is y = –cos(x) + 7.
37

c =

Question illustration
A
1 / 2
B
1
C
3 / 2
D
2
38

Question text not available

Answers:
Blank 1:1
Blank 2:0
39

The amplitude is . The vertical shift is . An equation for this graph is y = .

Answers:
Part 1:1
Part 2:0
40

c = ,

Answer:

8

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