AnswersAlgebra 2 MP 234 CHSModeling with Periodic Functions

Modeling with Periodic Functions — Unit test Answers

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1
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What is the exact value of ?

Question illustration
A
–1
B
Negative StartRoot 2 EndRoot
Option B
C
1
D
StartRoot 2 EndRoot
Option D
2
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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.
3

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
4

The angle measures associated with which set of ordered pairs share the same reference angle?

A
(Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half)
Option B
C
(Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Option D
5

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
6

What is the equation of the graph below?

Question illustration
A
y = sec(x) + 2
B
y = csc(x) + 2
C
y = csc(x + 2)
D
y = sec(x + 2)
7

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.
8

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Question illustration
A
Reflect the graph of the first function across the x-axis, translate it units to the left, and translate it 2 units up.
Option A
B
Reflect the graph of the first function across the x-axis, translate it units to the right, and translate it 2 units up.
Option B
C
Reflect the graph of the first function across the line , translate it units to the left, and translate it 2 units up.
Option C
D
Reflect the graph of the first function across the line , translate it units to the right, and translate it 2 units up.
Option D
9

Which is the graph of y = cos(x) + 3?

A
On a coordinate plane, a cosine curve has a maximum of 3 and a minimum of negative 3.
Option A
B
On a coordinate plane, a cosine curve has a maximum of 4 and a minimum of negative 2.
Option B
C
On a coordinate plane, a cosine curve has a maximum of negative 2 and a minimum of negative 4.
Option C
D
On a coordinate plane, a cosine curve has a maximum of 6 and a minimum of negative 0.
Option D
10

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
11

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
12

Which of the following is the equation of the function below?

Question illustration
A
y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option A
B
y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.
Option B
C
y equal to 0 point 5 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.
Option C
D
y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.
Option D
13

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
14

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
15

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

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