AnswersAlgebra 2 MP 234 CHSModeling with Periodic Functions

Modeling with Periodic Functions — Unit test Answers

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If , which equation represents ?

Question illustration
A
cotangent theta = StartFraction StartRoot 15 EndRoot Over 8 EndFraction
Option A
B
cotangent theta = StartFraction StartRoot 15 EndRoot Over 7 EndFraction
Option B
C
cotangent theta = StartFraction 7 StartRoot 15 EndRoot Over 15 EndFraction
Option C
D
cotangent theta = StartFraction 8 StartRoot 15 EndRoot Over 15 EndFraction
Option D
2
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Which function will have a y-intercept at –1 and an amplitude of 2?

A
f (x) = negative sine (X) minus 1
Option A
B
f (x) = negative 2 sine (x) minus 1
Option B
C
f (x) = negative cosine (x)
Option C
D
f (x) = negative 2 cosine (x) minus 1
Option D
3

Which of the following best explains the value of on the unit circle below?

Question illustration
A
The length opposite the angle is the vertical distance from the x-axis on the graph.
Option A
B
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Option B
C
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Option C
D
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Option D
4

If , which of the following represents approximate values of and , for ?

Question illustration
A
sine theta almost-equals 0.9511; tangent theta almost equals 0.3249
Option A
B
sine theta almost-equals 0.9511; tangent theta almost equals 3.0780
Option B
C
sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955
Option C
D
sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731
Option D
5

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . Which of the following is the graph of this equation?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
Option D
6

What is the equation of the graph below?

Question illustration
A
y = sine (x + 90 degrees)
Option A
B
y = cosine (x + 90 degrees)
Option B
C
y = sine (x + 45 degrees)
Option C
D
y = cosine (x + 45 degrees)
Option D
7

Which of the following are in the correct order from least to greatest?

A
, , 80°, , 38°
Option A
B
38°, 80°, , ,
Option B
C
38°, , 80°, ,
Option C
D
, 38°, 80°, ,
Option D
8

Which function describes the graph below?

Question illustration
A
f (x) = 6 cosine (x)
Option A
B
f (x) = 3 cosine (x) + 3
Option B
C
f (x) = 6 sine (x)
Option C
D
f (x) = 3 sine (x) + 3
Option D
9

Which of the following could be the equation of the function below?

Question illustration
A
y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2
Option A
B
y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2
Option B
C
y = 0.5 cosine (4 (x + pi)) + 2
Option C
D
y = 0.5 cosine (2 (x minus pi)) minus 2
Option D
10

What is the simplest form of the expression below?

Question illustration
A
sec
Option A
B
cot
Option B
C
csc
Option C
D
tan
Option D
11

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

A
h = negative 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option A
B
h = negative 10 sine (Pi t) + 35
Option B
C
h = 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option C
D
h = 10 sine (Pi t) + 35
Option D
12

What is the period of the function ?

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
13

What are the values of m and in the diagram below?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
14

Which is an x-intercept of the graph of the function ?

Question illustration
A
(minus StartFraction 2pi over 3 EndFraction , 0)
Option A
B
(minus StartFraction pi over 3 EndFraction , 0)
Option B
C
(StartFraction pi over 6 EndFraction , 0)
Option C
D
(StartFraction 5pi over 6 EndFraction , 0)
Option D
15

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

A
It is the graph of y = sec(x) shifted 3 units right and 7 units up.
B
It is the graph of y = sec(x) shifted 3 units left and 7 units up.
C
It is the graph of y = sec(x) shifted 3 units left and 7 units down.
D
It is the graph of y = sec(x) shifted 3 units right and 7 units down.
16

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 3 by 2 at (3 pi by 2, comma negative 3 by 2 ) and (negative pi by 2 by negative 3 by 2) and y equals negative 5 by 2 at ( pi by 2 comma negative 5 by 2) and (negative 3 pi by 2 comma negative 5 by 2).
Option A
B
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (3 pi by 2 comma negative 1) and (negative pi by 2 comma negative 1) and y equals negative 3 at (pi by 2 comma negative 3) and (negative 3 pi by 2 comma negative 3).
Option B
C
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 at (pi comma negative 1) and (negative pi comma negative 1) and y equals negative 3 at (0 comma negative 3).
Option C
D
On a coordinate plane, the x axis ranges from negative 2 pi to 2 pi with an interval of pi units and the y axis ranges from negative 5 to 1 with an interval of 1 unit. The graph is 2 pi periodic with asymptotes at x equals plus or minus n pi. It touches the lines y equals negative 1 point 8 at (0 comma negative 1 point 8) and y equals negative 2 point 2 at (pi comma negative 2 point 2) and (negative pi comma negative 2 point 2).
Option D
17

The point P(x, y) is on the terminal ray of angle . If is between radians and radians and csc = , what are the coordinates of P(x, y)?

Question illustration
A
P(, –2)
Option A
B
P (, –2)
Option B
C
P(–2, )
Option C
D
P(–2, )
Option D
18

What is the approximate length of arc s on the circle below? Use 3.14 for . Round your answer to the nearest tenth.

Question illustration
A
14.1 in.
B
22.5 in.
C
42.3 in.
D
56.5 in.
19

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

Question illustration
A
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option A
B
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option B
C
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option C
D
a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up
Option D
20

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

A
0.4 radian
B
1.0 radian
C
2.7 radians
D
5.0 radians

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