1
Convert to radian measure, giving the answer in terms of .
Choose one answer.
A.
B.
C.
D.
.
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Question 2
Convert radians to degree measure.
Choose one answer.
A.
B.
C.
D.
.
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Question 3
If a turntable rotates at 75 revolutions per minute, what is its angular speed (in radians per second)?
Choose one answer.
A. radians/second
B. radians/second
C. radians/second
D. radians/second
.
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Question 4
If the minute hand of a clock is 8 inches long, what distance will its tip move in 12 minutes?
Choose one answer.
A. in.
B. in.
C. in.
D. in.
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Question 5
Find the measures of two angles that are coterminal with an angle of measure . One of your answers should be positive and the other negative.
Choose one answer.
A. ,
B. ,
C. ,
D. ,
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Question 6
Find the reference angle for an angle of measure .
Choose one answer.
A.
B.
C.
D.
.
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Question 7
The hypotenuse of a right triangle measures 10 units. One of its non-right angles measures . Find the measure of the side opposite of that angle. Round your answer to the nearest hundredth.
Choose one answer.
A. 6.75
B. 8.29
C. 5.59
D. 5.29
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Question 8
One leg of a right triangle measures 6 units. The angle adjacent to that leg measures radians. Find the measure of the hypotenuse of the triangle to the nearest hundredth.
Choose one answer.
A. 0.15
B. 0.06
C. 6.49
D. 15.68
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Question 9
Find the coordinates of a point on a circle with radius 12 corresponding to an angle of . Leave your answer in terms of sine and cosine, and write the answer as an ordered pair.
Choose one answer.
A. (15 cos(), 15 sin())
B. (15 sin(), 15 cos())
C. (cos(),sin())
D. (sin(), cos())
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Question 10
Find the coordinates of a point on a circle with radius 8 corresponding to an angle of . Leave your answer in terms of sine and cosine, and write the answer as an ordered pair.
Choose one answer.
A. (sin(), cos())
B. (8sin(),8cos())
C. (cos(),sin())
D. (8 cos(),8sin())
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Question 11
Given that , find and .
Choose one answer.
A. ,
B. ,
C. ,
D. ,
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Question 12
Given that , find and .
Choose one answer.
A. and
B. and
C. and
D. and
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Question 13
A 12-foot ladder leans against a building, making a angle with the ground. To the nearest hundredth of a foot, how high does the ladder reach on the building?
Choose one answer.
A. 9.19 feet
B. 3.15 feet
C. 11.58 feet
D. 7.7 feet
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Question 14
Three-fourths of a mile from the base of a building, its angle of elevation is found to be 8 degrees from the ground. How tall is the building, to the nearest thousandth mile?
Choose one answer.
A. 0.105 miles tall
B. 0.104 miles tall
C. 0.743 miles tall
D. 5.335 miles tall
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Question 15
A building has an observation tower on top of it. From a location 100 feet from the base of the building, the angle of elevation to the top of the building is , and the angle of elevation to the top of the observation tower is . How tall is the observation tower, to the nearest hundredth?
Choose one answer.
A. 9.96 feet
B. 100.00 feet
C. 25.69 feet
D. 33.07 feet
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Question 16
Find exact values for the (i) sine, (ii) cosine, and (iii) tangent of .
Choose one answer.
A. (i) (ii) (iii)
B. (i) (ii) (iii)
C. (i) (ii) (iii)
D. (i) (ii) (iii)
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Question 17
Find exact values for the (i)sine, (ii) cosine, and (iii) tangent of .
Choose one answer.
A. (i) (ii) \frac{1}{2 (iii)
B. (i) (ii) (iii)
C. (i) (ii) (iii)
D. (i) (ii) (iii)
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Question 18
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
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Question 19
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 20
A ceiling fan with 16 inch blades rotates at 45 rpm. What is its angular speed, in rad/min?
Choose one answer.
A. rad/min
B. rad/min
C. rad/min
D. rad/min
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Question 21
A ceiling fan with 16 in blades rotates at 45 rpm. Find the linear speed of the tips of the blades in in/min.
Choose one answer.
A. in/min
B. 720 in/min
C. in/min
D. 1440 in/min
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Question 22
Which of the following is equal to ?
Choose one answer.
A.
B.
C.
D.
.
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Question 23
From the top of a 250 ft. tall lighthouse to a ship in the sea, the angle of depression is . How far from the lighthouse is the ship, exactly?
Choose one answer.
A. 500 ft
B. ft
C. 125 ft
D. ft
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Question 24
If , find (i) and (ii).
Choose one answer.
A.
B.
C.
D.
.
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Question 25
Pittsburgh and Miami lie on approximately the same meridian, with Pittsburgh at and Miami at . If the radius of the earth is 3960 miles, what is the distance between the two cities?
Choose one answer.
A. miles
B. miles
C. miles
D. miles
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Question 26
Which of the following describes how to transform the graph of y = sin(x) to create the graph of y = sin(x - 3)?
Choose one answer.
A. Shift the graph down by 3 units.
B. Shift the graph up by 3 units.
C. Shift the graph right by 3 units.
D. Shift the graph left by 3 units.
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Question 27
What is the domain of the function ?
Choose one answer.
A.
B.
C.
D.
.
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Question 28
What is the range of the function ?
Choose one answer.
A. (2,4)
B. [2,4]
C. [-1,1]
D.
.
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Question 29
Identify the amplitude, period, and phase (horizontal) shift for the function .
Choose one answer.
A. amplitude = , period = , phase shift =
B. amplitude = , period = , phase shift =
C. amplitude = 2, period = , phase shift =
D. amplitude = , period = , phase shift =
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Question 30
Find the midline shift of the function .
Choose one answer.
A. 9 units up
B. 9 units down
C. 3 units up
D. 3 units down
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Question 31
For a function of the form , which of the following is true?
(i) The amplitude is .
(ii) The period is .
(iii) The phase shift is -b.
Choose one answer.
A. (i), (ii), and (iii)
B. (i) only
C. (i) and (ii) only
D. (i) and (iii) only
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Question 32
Which of the following represents a sine curve with amplitude 2 and period ?
Choose one answer.
A.
B.
C.
D.
.
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Question 33
Which of the following represents a cosine curve with a phase shift units to the left and amplitude 4?
Choose one answer.
A.
B.
C.
D.
.
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Question 34
Which of the following represents a cosine curve with phase shift to the right and period ?
Choose one answer.
A.
B.
C.
D.
.
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Question 35
A patient's blood pressure is modeled by the function . Systolic blood pressure is the maximum value of this function and diastolic pressure s the minimum value. If blood pressure is written as systolic/diastolic, what is the blood pressure for the given patient?
Choose one answer.
A. 50/160
B. 85/135
C. 135/85
D. 160/50
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Question 36
In one 12-hour period, the tide on a beach starts at mean sea level, rises to 21 ft above sea level, drops to 21 ft below sea level, and then returns to mean sea level. Find the equation that best represents the height of the tide above mean sea level at time t.
Choose one answer.
A.
B.
C.
D.
.
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Question 37
A Ferris wheel with diameter 60 feet takes 4 minutes to complete a full rotation. Passengers board from a platform 8 feet above the ground. How high above the ground is a passenger after 2.5 minutes, to the nearest hundredth?
Choose one answer.
A. 59.21 ft
B. 16.79 ft
C. 35.95 ft
D. 40.05 ft
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Question 38
Find the exact value of , if it is defined.
Choose one answer.
A.
B.
C.
D. Undefined
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Question 39
Find the exact value of , if it is defined.
Choose one answer.
A. Undefined
B.
C.
D.
.
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Question 40
Find the exact value of , if it is defined.
Choose one answer.
A.
B. Undefined
C.
D.
.
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Question 41
For , which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D. x
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Question 42
Evaluate , if it is defined.
Choose one answer.
A.
B. Undefined
C.
D.
.
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Question 43
Evaluate , if it is defined.
Choose one answer.
A.
B.
C.
D.
.
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Question 44
If an observer views the space shuttle launch from a spot 2 miles away from the launch, express the viewing angle of elevation as a function of the shuttle's height above the ground.
Choose one answer.
A.
B.
C.
D.
.
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Question 45
Evaluate exactly.
Choose one answer.
A.
B.
C.
D.
.
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Question 46
A cork floats on a lake, bobbing in simple harmonic motion. Its displacement above the bottom of the lake is given by . At its lowest point, how far is the cork above the lake bottom?
Choose one answer.
A. 7.8 ft
B. 8 ft
C. 0.2 ft
D. 8.2 ft
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Question 47
A certain stock started at a high value of $9 per share and has been oscillating above and below the average value, decreasing by 3% per year. However, the average value started at $6 per share and has grown linearly by 60 cents per year. Which of the following represents the equation for the midline and amplitude of this stock?
Choose one answer.
A.
B.
C.
D.
.
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Question 48
A certain stock started at a high value of $9 per share and has been oscillating above and below the average value, decreasing by 3% per year. However, the average value started at $6 per share and has grown linearly by 60 cents per year. Find the equation S(t) for the value of the stock after t years.
Choose one answer.
A.
B.
C.
D.
.
.
Question 49
Find an exact value of .
Choose one answer.
A.
B.
C.
D.
.
.
Question 50
Find an exact value for .
Choose one answer.
A.
B.
C.
D.
.
.
Question 51
Find an exact value for .
Choose one answer.
A.
B.
C.
D.
.
.
Question 52
Which answer rewrites the following as the sine, cosine, or tangent of a single angle: ?
Choose one answer.
A.
B.
C.
D.
.
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Question 53
Which answer rewrites the following as the sine, cosine, or tangent of a single angle: ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 54
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 55
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 56
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 57
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 58
Which answer rewrites the following, using only powers of and : ?
Choose one answer.
A.
B.
C.
D.
.
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Question 59
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 60
Which of the following is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 61
Which of the following is equal to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 62
Which of the following is equal to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 63
The position of a weight attached to a spring at time t is described by the function . What is the maximum height of the weight, and when is the maximum height first reached?
Choose one answer.
A. 8 in, 12 seconds
B. 16 in, 0.4 seconds
C. 8 in, 0.04 seconds
D. 16 in, 12 seconds
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Question 64
Find all solutions of the equation in the interval .
Choose one answer.
A.
B.
C.
D.
.
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Question 65
Find all solutions of the equation .
Choose one answer.
A. or , k any integer
B. , k any integer
C. , k any integer
D. , k any integer
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Question 66
Solve the equation .
Choose one answer.
A. No solution
B. , k any integer
C. , k any integer
D. , k any integer
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Question 67
Solve the equation on the interval .
Choose one answer.
A.
B.
C.
D.
.
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Question 68
Solve the equation .
Choose one answer.
A. , or
B.
C.
D. No solution
.
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Question 69
Use a calculator to find the solutions to in the interval , accurate to 4 decimal places.
Choose one answer.
A.
B.
C.
D.
.
.
Question 70
The phase of the moon can be measured astronomically by the fraction of the lunar disc that is lit. If represents the angle between the sun, earth, and moon, then the phase of the moon can be represented by the function . Determine the angle that corresponds to a full moon (P = 1).
Choose one answer.
A.
B.
C.
D.
.
.
Question 71
The phase of the moon can be measured astronomically by the fraction of the lunar disc that is lit. If represents the angle between the sun, earth, and moon, then the phase of the moon can be represented by the function . Determine the angle that that corresponds to a crescent moon (P = .25).
Choose one answer.
A.
B.
C.
D.
.
.
Question 72
Which algebraic expression is equivalent to ?
Choose one answer.
A.
B.
C.
D.
.
.
Question 73
A boat sails for 2 hours at 30 mph in a direction of . How far south has it sailed, to the nearest mile?
Choose one answer.
A. 52 miles
B. 30 miles
C. 9 miles
D. 60 miles
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Question 74
A satellite orbiting the earth can be viewed from two cities simultaneously. The two cities are 300 miles apart. At an instant when the satellite is overhead both cities, its angle of elevation is from the first city and from the second. What is its distance from the first city, to the nearest mile?
Choose one answer.
A. 92 miles
B. 315 miles
C. 418 miles
D. 91 miles
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Question 75
Solve the triangle for the missing sides, or state that no triangle satisfies the condition. Angle A = , a = 70 (across from angle A) and b= 122.
Choose one answer.
A. Angle B = 1.59.
B. Angle B = 38.
C. Angle B = 1.17.
D. No triangle
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Question 76
A 3500 ft. mountain is inclined from the horizontal (i.e. the face of the mountain and the ground form a angle). A cable car is installed at a point 1000 ft. from the base of the mountain. What is the minimum amount of cable required to reach the top of the mountain, to the nearest foot?
Choose one answer.
A. 4000 ft
B. 3623 ft
C. 1035 ft
D. Not enough information is given.
.
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Question 77
is a point given in polar coordinates. Find its rectangular coordinates.
Choose one answer.
A. (0, -4)
B. (4, 0)
C. (0, 4)
D. (-4, 0)
.
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Question 78
For the point (2, 2) with rectangular coordinates, find two pairs of polar coordinates with .
Choose one answer.
A.
B.
C.
D.
.
.
Question 79
In which quadrant of the Cartesian coordinate plane would the polar coordinate point lie?
Choose one answer.
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
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Question 80
Which of the following accurately writes the polar equation in rectangular form?
Choose one answer.
A.
B.
C.
D.
.
.
Question 81
Which of the following writes the equation in polar coordinates?
Choose one answer.
A.
B.
C.
D.
.
.
Question 82
Determine the values of at which maximum r-values occur on the polar equation . (Note that a maximum r value occurs at a point that is the maximum distance from the pole.)
Choose one answer.
A.
B.
C.
D.
.
.
Question 83
How many petals does the rose curve have?
Choose one answer.
A. 1
B. 3
C. 4
D. 6
.
.
Question 84
Find the cube roots of .
Choose one answer.
A.
B.
C.
D.
.
.
Question 85
Express the complex number in trigonometric form.
Choose one answer.
A.
B.
C.
D.
.
.
Question 86
Find the cube roots of 8, expressed in form.
Choose one answer.
A.
B.
C.
D.
.
.
Question 87
Let and let . Find .
Choose one answer.
A.
B.
C.
D.
.
.
Question 88
Let and . Find .
Choose one answer.
A.
B.
C. -18
D. 30
.
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Question 89
Find the angle between the vectors and to the nearest tenth of a degree.
Choose one answer.
A.
B.
C.
D.
.
.
Question 90
A man leaves home, walks 4 miles west and then 2 miles southeast. If he returns directly home (i.e. walking the straight line from his current location to his home) what is his total distance traveled, to the nearest hundredth mile?
Choose one answer.
A. 4.47 miles
B. 10.47 miles
C. 2.95 miles
D. 8.95 miles
.
.
Question 91
One rope pulls a heavy weight directly easy with a force of 22N. Another rope pulls the weight directly north with a force of 45 N. Find the resultant force on the weight.
Choose one answer.
A. 50N
B. 23N
C. 67N
D. 2500N
.
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Question 92
An airplane heads due north at 300 mph. There is a 40 mph crosswind flowing from the southwest . What are the true speed and direction of the airplane? (Bear in mind that direction is measured from North in the clockwise direction.)
Choose one answer.
A.
B.
C.
D.
.
.
Question 93
Find a parametrization of the line through the points (4, 1) and (5, -2).
Choose one answer.
A. x = 4 + t, y = 1 - 3t
B. x = 4 - 3t, y = 1 + t
C. x = 5 - t, y = -2 + 3t
D. x = -4 + t, y = -1 - 3t
.
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Question 94
Eliminate the parameter to write in rectangular coordinate form.
Choose one answer.
A.
B.
C.
D.
.
.
Question 95
Find a parametrization of the line segment beginning at the point (3, 2) and ending at the point (-1, 4). Specify the bounds for t.
Choose one answer.
A.
B.
C.
D.
.
.
Question 96
A light is placed on the edge of a wheel of radius 10. Find a parametric equation for the position of the light after the wheel has rotated through an angle of .
Choose one answer.
A.
B.
C.
D.
.
.
Question 97
In a foot race, Paul can sprint at 20 ft/sec, and Ronald can sprint at 22 ft/sec. Ronald is given a 12 second head start. Parametric equations to represent the race are given by . Graph the equations simultaneously and determine who is ahead after 8 seconds, and by how much.
Choose one answer.
A. Ronald is ahead by 4 ft.
B. Ronald is ahead by 8 ft.
C. The race is tied.
D. Paul is ahead by 2 ft.
.
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Question 98
In a foot race, Paul can sprint at 20 ft/sec, and Ronald can sprint at 22 ft/sec. Ronald is given a 12 second head start. Parametric equations to represent the race are given by . Graph the equations simultaneously and determine when the race is tied.
Choose one answer.
A. At t = 2.
B. At t = 4.
C. At t= 6.
D. It is never tied.
.
.
Question 99
What is the domain of the function ?
Choose one answer.
A.
B.
C.
D. All real numbers
.
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Question 100
What is the range of the function ?
Choose one answer.
A. All real numbers
B.
C.
D.
.
.