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Deck 33: Solving Trigonometric Equations
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Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)No solution
C)
D)
E)
A)
B)No solution
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)0
C)
D)
E)
A)
B)0
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the following equation.
Secx - 2 = 0
A)
and 
,where n is a integer
B)
and 
,where n is a integer
C)
and 
,where n is a integer
D)
and 
,where n is a integer
E)
and 
,where n is a integer
Secx - 2 = 0
A)
and ,where n is a integerB)
and ,where n is a integerC)
and ,where n is a integerD)
and ,where n is a integerE)
and ,where n is a integer Question
Use a graphing utility to graph the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use inverse functions where needed to find all solutions of the equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to graph the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use inverse functions where needed to find all solutions of the equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by 
,where y is the displacement (in meters)and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0)for 
. 
A)0.05sec,0.49sec,0.94sec
B)0.05sec,0.05sec,0.94sec
C)-0.40sec,0.49sec,0.94sec
D)-0.40sec,0.49sec,-0.40sec
E)0.05sec,-0.40sec,0.94sec
,where y is the displacement (in meters)and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0)for . A)0.05sec,0.49sec,0.94sec
B)0.05sec,0.05sec,0.94sec
C)-0.40sec,0.49sec,0.94sec
D)-0.40sec,0.49sec,-0.40sec
E)0.05sec,-0.40sec,0.94sec
Question
The table shows the average daily high temperatures in Houston H (in degrees Fahrenheit)for month t,with t = 1 corresponding to January. 
Select the correct scatter plot from the above data.
A)
B)
C)
D)
E)
Select the correct scatter plot from the above data.
A)
B)
C)
D)
E)
Question
Solve the following equation. 
A)
,where n is an integer
B)
,where n is an integer
C)
,where n is an integer
D)
,where n is an integer
E)
,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Question
Solve the following equation. 
A)
,where n is an integer
B)
,where n is an integer
C)
,where n is an integer
D)
,where n is an integer
E)
,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Question
Use a graphing utility to graph the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to graph the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use inverse functions where needed to find all solutions of the equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Which of the following is a solution to the given equation?
Cscx + 2 = 0
A)
B)
C)
D)
E)
Cscx + 2 = 0
A)
B)
C)
D)
E)
Question
Which of the following is a solution to the given equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to graph the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine whether the statement is true or false.Justify your answer.
The equation
has four times the number of solutions in the interval [0,2π)as the equation 
.
A)False
B)True
The equation
has four times the number of solutions in the interval [0,2π)as the equation .
A)False
B)True
Question
Solve the following equation. 
A)
,where n is an integer
B)
,where n is an integer
C)
,where n is an integer
D)
,where n is an integer
E)
,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Question
Using the grid provided,sketch the graph of the given function in the interval (-5,5)and then determine the x-intercepts,if any. 
A)(-3,0)and (1,0)
B)(-2,0)
C)(-2,0)and (2,0)
D)no x-intercepts
E)(-4,0), (0,0),and (4,0)
A)(-3,0)and (1,0)
B)(-2,0)
C)(-2,0)and (2,0)
D)no x-intercepts
E)(-4,0), (0,0),and (4,0)
Question
Which of the following is a solution to the given equation?
Cscx - 2 = 0
A)
B)
C)
D)
E)
Cscx - 2 = 0
A)
B)
C)
D)
E)
Question
A Ferris wheel is built such that the height h (in feet)above the ground of a seat on the wheel at time t (in seconds)can be modeled by 
.The wheel makes one revolution every 36 seconds and the ride begins when t = 0.During the first 36 seconds of the ride,when will a person,who starts at the bottom of the Ferris wheel,be 67 feet above the ground?
A)9 seconds and 22 seconds
B)9 seconds and 27 seconds
C)10 seconds and 22 seconds
D)9 seconds and 17 seconds
E)10 seconds and 17 seconds
.The wheel makes one revolution every 36 seconds and the ride begins when t = 0.During the first 36 seconds of the ride,when will a person,who starts at the bottom of the Ferris wheel,be 67 feet above the ground? A)9 seconds and 22 seconds
B)9 seconds and 27 seconds
C)10 seconds and 22 seconds
D)9 seconds and 17 seconds
E)10 seconds and 17 seconds
Question
Use the Quadratic Formula to solve the given equation on the interval [ 
);then use a graphing utility to approximate the angle x.Round answers to three decimal places. 
A)x = 1.229,1.433
B)x = 1.227,1.422
C)x = 1.233,1.469
D)x = 1.231,1.451
E)x = 1.235,1.480
);then use a graphing utility to approximate the angle x.Round answers to three decimal places. A)x = 1.229,1.433
B)x = 1.227,1.422
C)x = 1.233,1.469
D)x = 1.231,1.451
E)x = 1.235,1.480
Question
Solve the multiple-angle equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to approximate the solutions (to three decimal places)of the given equation in the interval [0,2π). 
A)x = 1.624,1.932,5.776,5.997
B)x = 1.101,2.118,3.982,5.104
C)x = 1.571,3.990,4.712,5.435
D)x = 1.055,3.785,4.652,5.721
E)x = 1.484,3.799,4.626,5.490
A)x = 1.624,1.932,5.776,5.997
B)x = 1.101,2.118,3.982,5.104
C)x = 1.571,3.990,4.712,5.435
D)x = 1.055,3.785,4.652,5.721
E)x = 1.484,3.799,4.626,5.490
Question
The monthly sales S (in hundreds of units)of baseball equipment for an Internet sporting goods site are approximated by 
where t is the time (in months),with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.
A)April through August
B)July through May
C)June through August
D)April through July
E)May through July
where t is the time (in months),with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.A)April through August
B)July through May
C)June through August
D)April through July
E)May through July
Question
Use a graphing utility to approximate the solutions (to three decimal places)of the given equation in the interval 
. 
A)x = 0.398
B)x = 1.336
C)x = 0.094
D)x = 0.73
E)x = 0.139
. A)x = 0.398
B)x = 1.336
C)x = 0.094
D)x = 0.73
E)x = 0.139
Question
Use inverse functions where needed to find all solutions (if they exist)of the given equation on the interval [0,2π). 
A)
B)
C)
D)
E)solution does not exist
A)
B)
C)
D)
E)solution does not exist
Question
Find all solutions of the following equation in the interval [0,2π). 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the multiple-angle equation. 
A)
,where n is an integer
B)
,where n is an integer
C)
,where n is an integer
D)
,where n is an integer
E)
,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Question
The horizontal distance d (in feet)traveled by a projectile with an initial speed of v feet per second is modeled by 
, where θ is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of
.Round to the nearest foot.
A)260
B)346
C)173
D)303
E)87
, where θ is the angle at which the projectile is launched.Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of
.Round to the nearest foot.A)260
B)346
C)173
D)303
E)87
Question
Which of the following is a solution to the given equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 33: Solving Trigonometric Equations
1
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Find all solutions of the following equation in the interval [0,2π).
A)
B)No solution
C)
D)
E)
A)
B)No solution
C)
D)
E)
No solution
3
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Find all solutions of the following equation in the interval [0,2π).
A)
B)0
C)
D)
E)
A)
B)0
C)
D)
E)
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7
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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18
Solve the following equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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21
Solve the following equation.
Secx - 2 = 0
A) and ,where n is a integer
B) and ,where n is a integer
C) and ,where n is a integer
D) and ,where n is a integer
E) and ,where n is a integer
Secx - 2 = 0
A)
and ,where n is a integerB)
and ,where n is a integerC)
and ,where n is a integerD)
and ,where n is a integerE)
and ,where n is a integer Unlock Deck
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22
Use a graphing utility to graph the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
Solve the multiple-angle equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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25
Solve the multiple-angle equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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26
Use a graphing utility to graph the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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27
Solve the multiple-angle equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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28
Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 54 flashcards in this deck.
Unlock Deck
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29
A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by ,where y is the displacement (in meters)and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0)for .
A)0.05sec,0.49sec,0.94sec
B)0.05sec,0.05sec,0.94sec
C)-0.40sec,0.49sec,0.94sec
D)-0.40sec,0.49sec,-0.40sec
E)0.05sec,-0.40sec,0.94sec
,where y is the displacement (in meters)and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0)for . A)0.05sec,0.49sec,0.94sec
B)0.05sec,0.05sec,0.94sec
C)-0.40sec,0.49sec,0.94sec
D)-0.40sec,0.49sec,-0.40sec
E)0.05sec,-0.40sec,0.94sec
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30
The table shows the average daily high temperatures in Houston H (in degrees Fahrenheit)for month t,with t = 1 corresponding to January.
Select the correct scatter plot from the above data.
A)
B)
C)
D)
E)
Select the correct scatter plot from the above data.
A)
B)
C)
D)
E)
Unlock Deck
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31
Solve the following equation.
A) ,where n is an integer
B) ,where n is an integer
C) ,where n is an integer
D) ,where n is an integer
E) ,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Unlock Deck
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32
Solve the following equation.
A) ,where n is an integer
B) ,where n is an integer
C) ,where n is an integer
D) ,where n is an integer
E) ,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Unlock Deck
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Unlock Deck
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33
Use a graphing utility to graph the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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34
Use a graphing utility to graph the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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35
Solve the multiple-angle equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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36
Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 54 flashcards in this deck.
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37
Which of the following is a solution to the given equation?
Cscx + 2 = 0
A)
B)
C)
D)
E)
Cscx + 2 = 0
A)
B)
C)
D)
E)
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38
Which of the following is a solution to the given equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Use a graphing utility to graph the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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40
Determine whether the statement is true or false.Justify your answer.
The equation has four times the number of solutions in the interval [0,2π)as the equation .
A)False
B)True
The equation
has four times the number of solutions in the interval [0,2π)as the equation .
A)False
B)True
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41
Solve the following equation.
A) ,where n is an integer
B) ,where n is an integer
C) ,where n is an integer
D) ,where n is an integer
E) ,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Unlock Deck
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42
Using the grid provided,sketch the graph of the given function in the interval (-5,5)and then determine the x-intercepts,if any.
A)(-3,0)and (1,0)
B)(-2,0)
C)(-2,0)and (2,0)
D)no x-intercepts
E)(-4,0), (0,0),and (4,0)
A)(-3,0)and (1,0)
B)(-2,0)
C)(-2,0)and (2,0)
D)no x-intercepts
E)(-4,0), (0,0),and (4,0)
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43
Which of the following is a solution to the given equation?
Cscx - 2 = 0
A)
B)
C)
D)
E)
Cscx - 2 = 0
A)
B)
C)
D)
E)
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44
A Ferris wheel is built such that the height h (in feet)above the ground of a seat on the wheel at time t (in seconds)can be modeled by .The wheel makes one revolution every 36 seconds and the ride begins when t = 0.During the first 36 seconds of the ride,when will a person,who starts at the bottom of the Ferris wheel,be 67 feet above the ground?
A)9 seconds and 22 seconds
B)9 seconds and 27 seconds
C)10 seconds and 22 seconds
D)9 seconds and 17 seconds
E)10 seconds and 17 seconds
.The wheel makes one revolution every 36 seconds and the ride begins when t = 0.During the first 36 seconds of the ride,when will a person,who starts at the bottom of the Ferris wheel,be 67 feet above the ground? A)9 seconds and 22 seconds
B)9 seconds and 27 seconds
C)10 seconds and 22 seconds
D)9 seconds and 17 seconds
E)10 seconds and 17 seconds
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45
Use the Quadratic Formula to solve the given equation on the interval [ );then use a graphing utility to approximate the angle x.Round answers to three decimal places.
A)x = 1.229,1.433
B)x = 1.227,1.422
C)x = 1.233,1.469
D)x = 1.231,1.451
E)x = 1.235,1.480
);then use a graphing utility to approximate the angle x.Round answers to three decimal places. A)x = 1.229,1.433
B)x = 1.227,1.422
C)x = 1.233,1.469
D)x = 1.231,1.451
E)x = 1.235,1.480
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46
Solve the multiple-angle equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
Use a graphing utility to approximate the solutions (to three decimal places)of the given equation in the interval [0,2π).
A)x = 1.624,1.932,5.776,5.997
B)x = 1.101,2.118,3.982,5.104
C)x = 1.571,3.990,4.712,5.435
D)x = 1.055,3.785,4.652,5.721
E)x = 1.484,3.799,4.626,5.490
A)x = 1.624,1.932,5.776,5.997
B)x = 1.101,2.118,3.982,5.104
C)x = 1.571,3.990,4.712,5.435
D)x = 1.055,3.785,4.652,5.721
E)x = 1.484,3.799,4.626,5.490
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48
The monthly sales S (in hundreds of units)of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months),with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.
A)April through August
B)July through May
C)June through August
D)April through July
E)May through July
where t is the time (in months),with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.A)April through August
B)July through May
C)June through August
D)April through July
E)May through July
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49
Use a graphing utility to approximate the solutions (to three decimal places)of the given equation in the interval .
A)x = 0.398
B)x = 1.336
C)x = 0.094
D)x = 0.73
E)x = 0.139
. A)x = 0.398
B)x = 1.336
C)x = 0.094
D)x = 0.73
E)x = 0.139
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50
Use inverse functions where needed to find all solutions (if they exist)of the given equation on the interval [0,2π).
A)
B)
C)
D)
E)solution does not exist
A)
B)
C)
D)
E)solution does not exist
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51
Find all solutions of the following equation in the interval [0,2π).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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52
Solve the multiple-angle equation.
A) ,where n is an integer
B) ,where n is an integer
C) ,where n is an integer
D) ,where n is an integer
E) ,where n is an integer
A)
,where n is an integerB)
,where n is an integerC)
,where n is an integerD)
,where n is an integerE)
,where n is an integer Unlock Deck
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53
The horizontal distance d (in feet)traveled by a projectile with an initial speed of v feet per second is modeled by , where θ is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of .Round to the nearest foot.
A)260
B)346
C)173
D)303
E)87
, where θ is the angle at which the projectile is launched.Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of
.Round to the nearest foot.A)260
B)346
C)173
D)303
E)87
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54
Which of the following is a solution to the given equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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Unlock Deck
Unlock for access to all 54 flashcards in this deck.
