AnswersTX-Pre-CalculusUnit Test

Unit Test — Unit test Answers

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According to your graphing calculator, what is the approximate solution to the trigonometric inequality over the interval radians?

Question illustration
A
x is greater than equal to 0 but less than 1.3280
Option A
B
x is greater than equal to 0 but less than 1.6985
Option B
C
x is greater than equal to 0 but less than 1.9182
Option C
D
x is greater than equal to 0 but less than 2.4534
Option D
2
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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
3

What is the period of the function ?

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units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
4

Which of the following is the graph of ?

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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
5

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
6

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
7

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
8

An object is attached to a spring that is stretched and released. The equation models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.

Question illustration
A
0 seconds
B
1.38 seconds
C
4.62 seconds
D
8 seconds
9

Which sum or difference identity would you use to verify that sin (90° + q) = cos q?a.cos (a -b) = cos a cos b + sin a sin bb.sin (a +b) = sin a cos b + cos a sin bc.sin (a -b) = sin a cos b- cos a sin bd.cos (a +b) = cos a cos b - sin a sin b

A
A
B
B
C
C
D
D
10

Graph sinon the interval a.c.b.d.

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A
B
B
C
C
D
D
11

Assume that and . Find the exact value of if and . a.c.b.d.

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A
B
B
C
C
D
D
12

What is the solution to the trigonometric inequality over the interval radians?

Question illustration
A
x is greater than equal to 0 but less than StartFraction 3pi over 2 EndFraction
Option A
B
and
Option B
C
and
Option C
D
x is greater than StartFraction 3pi over 2 EndFraction but less than equal to 2pi
Option D
13

What is the range of ?

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

Evaluate a.c.b.d.

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A
B
B
C
C
D
D
15

Which shows all the exact solutions of ? Give your answer in radians.

Question illustration
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and
Option A
B
and
Option B
C
, , , and
Option C
D
, , , and
Option D
16

In which of the following intervals does the trigonometric inequality always hold true?

Question illustration
A
radians
Option A
B
radians
Option B
C
radians
Option C
D
radians
Option D
17

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
18

Which is equivalent to ? Give your answer in radians.

Question illustration
A
0
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
19

According to your graphing calculator, what is the approximate solution to the trigonometric inequality over the interval radians?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
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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