MA003-FinalExam-Answers

Convert

to radian measure, giving the answer in terms of

Choose one answer.

	A.
	B.
	C.
	D.

Question 2

Convert

radians to degree measure.

Choose one answer.

	A.
	B.
	C.
	D.

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

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.

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. ,

Question 6

Find the reference angle for an angle of measure

Choose one answer.

	A.
	B.
	C.
	D.

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

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

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())

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())

Question 11

Given that

, find

and

Choose one answer.

	A. ,
	B. ,
	C. ,
	D. ,

Question 12

Given that

, find

and

Choose one answer.

	A. and
	B. and
	C. and
	D. and

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

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

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

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)

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)

Question 18

Which of the following is equivalent to

Choose one answer.

	A.
	B.
	C.
	D.

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

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

Question 22

Which of the following is equal to

Choose one answer.

	A.
	B.
	C.
	D.

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

Question 24

, find (i)

and (ii)

Choose one answer.

	A.
	B.
	C.
	D.

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

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.

Question 27

What is the domain of the function

Choose one answer.

	A.
	B.
	C.
	D.

Question 28

What is the range of the function

Choose one answer.

	A. (2,4)
	B. [2,4]
	C. [-1,1]
	D.

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 =

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

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

Question 32

Which of the following represents a sine curve with amplitude 2 and period

Choose one answer.

	A.
	B.
	C.
	D.

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.

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.

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

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.

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

Question 38

Find the exact value of

, if it is defined.

Choose one answer.

	A.
	B.
	C.
	D. Undefined

Question 39

Find the exact value of

, if it is defined.

Choose one answer.

	A. Undefined
	B.
	C.
	D.

Question 40

Find the exact value of

, if it is defined.

Choose one answer.

	A.
	B. Undefined
	C.
	D.

Question 41

For

, which of the following is equivalent to

Choose one answer.

	A.
	B.
	C.
	D. x

Question 42

Evaluate

, if it is defined.

Choose one answer.

	A.
	B. Undefined
	C.
	D.

Question 43

Evaluate

, if it is defined.

Choose one answer.

	A.
	B.
	C.
	D.

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.

Question 45

Evaluate

exactly.

Choose one answer.

	A.
	B.
	C.
	D.

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

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.

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.

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.

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

Question 64

Find all solutions of the equation

in the interval

Choose one answer.

	A.
	B.
	C.
	D.

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

Question 66

Solve the equation

Choose one answer.

	A. No solution
	B. , k any integer
	C. , k any integer
	D. , k any integer

Question 67

Solve the equation

on the interval

Choose one answer.

	A.
	B.
	C.
	D.

Question 68

Solve the equation

Choose one answer.

	A. , or
	B.
	C.
	D. No solution

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

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

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

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.

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)

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

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

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

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

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.

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

Question 100

What is the range of the function

Choose one answer.

	A. All real numbers
	B.
	C.
	D.