AnswersAlgebra II - MA3111 CRUnit Test

Unit Test — Unit test Answers

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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
2
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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
3

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

Question illustration
A
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
Option A
B
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
Option B
C
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
Option C
D
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Option D
4

Consider the relationship below, given .Which of the following best explains how this relationship and the value of sin can be used to find the other trigonometric values?

Question illustration
A
The values of sin and cos represent the legs of a right triangle with a hypotenuse of 1; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option A
B
The values of sin and cos represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
Option B
C
The values of sin and cos represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1, which can then be used to find all other values.
Option C
D
The values of sin and cos represent the legs of a right triangle with a hypotenuse of –1, since is in Quadrant II; therefore, solving for cos finds the unknown leg, and then all other trigonometric values can be found.
Option D
5

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
6

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.
7

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

Question illustration
A
(–5, 12)
B
(5, –12)
C
(–12, 5)
D
(12, –5)
8

Which of the following is true of the location of an angle, , whose tangent value is ?

Question illustration
A
has a 30-degree reference angle and is located in Quadrant II or IV
Option A
B
has a 30-degree reference angle and is located in Quadrant II or III
Option B
C
has a 60-degree reference angle and is located in Quadrant II or IV
Option C
D
has a 60-degree reference angle and is located in Quadrant II or III
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

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
11

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
12

What is the range of y = –3sin(x) – 4?

A
all real numbers
Option A
B
all real numbers
Option B
C
all real numbers
Option C
D
all real numbers
Option D
13

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
14

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
15

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
16

What is 270° converted to radians?

A
StartFraction pi Over 6 EndFraction
Option A
B
StartFraction 3 Over 2 EndFraction
Option B
C
StartFraction 3 pi Over 2 EndFraction
Option C
D
3
17

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
18

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A
h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5
Option A
B
h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
Option B
C
h = cosine (StartFraction pi Over 12 EndFraction t) + 9
Option C
D
h = cosine (StartFraction pi Over 6 EndFraction t) + 9
Option D
19

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
20

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

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