# Quiz 7: Analytic Trigonometry

Mathematics

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Q 6Q 6

Find all solutions of the equation.
A) for every integer n.
B) for every integer n.
C)1
D) for every integer n.
E) for every integer n.

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Q 8Q 8

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.
A)
B)
C)
D)
E)

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Q 9Q 9

On a cloudy day with D hours of daylight, the intensity of sunlight I (in calories/cm

^{ 2 }) may be approximated by where t = 0 corresponds to sunrise and I_{ m }is the maximum intensity. If D = 12, approximately how many hours after sunrise is ? Round your answer to two decimal places. A) B) C) D) E)no solutionFree

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Q 13Q 13

If a mass that is attached to a spring is raised y

_{ 0 }feet and released with an initial vertical velocity of v_{ 0 }ft / sec, then the subsequent position y of the mass is given by where t is time in seconds and is a positive constant. If y_{ 0 }= 2 and = 2, find the initial velocities that result in an amplitude of 4 feet. A) B) C) D) E)Free

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Q 16Q 16

A graph of for is shown in the figure. Find the exact values of the x-intercepts.
A)
B)
C)
D)
E)

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Q 17Q 17

A graph of for is shown in the figure. Find the exact values of the x-intercepts.
A)
B)
C)
D)
E)

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Q 22Q 22

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.
A)
B)
C)
D)
E)

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Q 25Q 25

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula where D is the depth (in kilometers) below the surface of the focal point of the earthquake. Approximate the depth D of the focal point of an earthquake with S = 3 m if a point on the surface of Earth 3 kilometers from the fault line moved 0.75 meters horizontally. Round the answer to the nearest hundredth.
A) km
B) km
C) km
D) km
E) km

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Q 31Q 31

Find all solutions of the equation.
A) for every integer n.
B)1
C) for every integer n.
D) for every integer n.
E) for every integer n.

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Q 33Q 33

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in November.
A)
B)
C)
D)
E)

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Q 34Q 34

On a clear day with D hours of daylight, the intensity of sunlight I (in calories/cm

^{ 2 }) may be approximated by where t = 0 corresponds to sunrise and I_{ m }is the maximum intensity. If D = 12, approximately how many hours after sunrise is ? Round your answer to two decimal places. A) B) C) D) E)no solutionFree

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Q 38Q 38

If a mass that is attached to a spring is raised y

_{ 0 }feet and released with an initial vertical velocity of v_{ 0 }ft / sec, then the subsequent position y of the mass is given by where t is time in seconds and is a positive constant. If y_{ 0 }= 2 and = 2, find the initial velocities that result in an amplitude of 4 feet. A) B) C) D) E)Free

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Q 41Q 41

A graph of for is shown in the figure. Find the exact values of the x-intercepts.
A)
B)
C)
D)
E)

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Q 42Q 42

A graph of for is shown in the figure. Find the exact values of the x-intercepts.
A)
B)
C)
D)
E)

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Q 47Q 47

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.
A)
B)
C)
D)
E)

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Q 50Q 50

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula where D is the depth (in kilometers) below the surface of the focal point of the earthquake. Approximate the depth D of the focal point of an earthquake with S = 3 m if a point on the surface of Earth 3 kilometers from the fault line moved 0.77 meters horizontally. Round the answer to the nearest hundredth.
A) km
B) km
C) km
D) km
E) km

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Q 56Q 56

Find all solutions of the equation.
A)1
B) for every integer n.
C) for every integer n.
D) for every integer n.
E) for every integer n.

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Q 58Q 58

The average monthly high temperature T (in ) in Augusta, Georgia, can be approximated using the function where t is in months and t = 1 corresponds to January. Calculate the average high temperature in July.
A)
B)
C)
D)
E)

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Q 59Q 59

On a cloudy day with D hours of daylight, the intensity of sunlight I (in calories/cm

^{ 2 }) may be approximated by where t = 0 corresponds to sunrise and I_{ m }is the maximum intensity. If D = 12, approximately how many hours after sunrise is ? Round your answer to two decimal places. A) B) C) D) E)no solutionFree

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Q 63Q 63

If a mass that is attached to a spring is raised y

_{ 0 }feet and released with an initial vertical velocity of v_{ 0 }ft / sec, then the subsequent position y of the mass is given by where t is time in seconds and is a positive constant. If y_{ 0 }= 1 and = 4, find the initial velocities that result in an amplitude of 5 feet. A) B) C) D) E)Free

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Q 66Q 66

A graph of for is shown in the figure. Find the exact values of the x-intercepts.
A)
B)
C)
D)
E)

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Q 67Q 67

A graph of for is shown in the figure. Find the exact values of the x-intercepts.
A)
B)
C)
D)
E)

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Q 72Q 72

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.
A)
B)
C)
D)
E)

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Q 75Q 75

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula where D is the depth (in kilometers) below the surface of the focal point of the earthquake. Approximate the depth D of the focal point of an earthquake with S = 5 m if a point on the surface of Earth 7 kilometers from the fault line moved 0.67 meters horizontally. Round the answer to the nearest hundredth.
A) km
B) km
C) km
D) km
E) km

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Q 81Q 81

Make the trigonometric substitution and a > 0. Use fundamental identities to simplify the resulting expression.
A)
B)
C)
D)
E)

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Q 82Q 82

Find all solutions of the equation.
A) for every integer n.
B) for every integer n.
C) for every integer n.
D) for every integer n.
E) for every integer n.

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Q 83Q 83

Find all solutions of the equation.
A) and for every integer n.
B) and for every integer n.
C) and for every integer n.
D) and for every integer n.
E) for every integer n.

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Q 86Q 86

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .
A)
B)
C)
D)
E)

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Q 90Q 90

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.
A)
B)
C)
D)
E)

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Q 97Q 97

Use the graph of f to find the simplest expression g(x) such that the equation f (x) = g (x) is an identity.
A)
B)
C)
D)
E)

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Q 98Q 98

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula where D is the depth (in kilometers) below the surface of the focal point of the earthquake. For the San Francisco earthquake of 1906, S was 6 meters and D was 3.05 kilometers. Approximate M for d = 9 kilometers. Round the answer to the nearest hundredth.
A) m
B) m
C) m
D) m
E) m

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Q 99Q 99

A golfer, centered in a b = 20-yard-wide straight fairway, hits a ball a = 290 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.
A)
B)
C)
D)
E)

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Q 106Q 106

Make the trigonometric substitution and a > 0. Use fundamental identities to simplify the resulting expression.
A)
B)
C)
D)
E)

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Q 107Q 107

Find all solutions of the equation.
A) for every integer n.
B) for every integer n.
C) for every integer n.
D) for every integer n.
E) for every integer n.

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Q 108Q 108

Find all solutions of the equation.
A) and for every integer n.
B) for every integer n.
C) and for every integer n.
D) and for every integer n.
E) and for every integer n.

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Q 111Q 111

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .
A)
B)
C)
D)
E)

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Q 115Q 115

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.
A)
B)
C)
D)
E)

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Q 122Q 122

Use the graph of f to find the simplest expression g(x) such that the equation f (x) = g (x) is an identity.
A)
B)
C)
D)
E)

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Q 123Q 123

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula where D is the depth (in kilometers) below the surface of the focal point of the earthquake. For the San Francisco earthquake of 1906, S was 5 meters and D was 3.07 kilometers. Approximate M for d = 9 kilometers. Round the answer to the nearest hundredth.
A) m
B) m
C) m
D) m
E) m

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Q 124Q 124

A golfer, centered in a b = 20-yard-wide straight fairway, hits a ball a = 270 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.
A)
B)
C)
D)
E)

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Q 131Q 131

Make the trigonometric substitution and a > 0. Use fundamental identities to simplify the resulting expression.
A)
B)
C)
D)
E)

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Q 132Q 132

Find all solutions of the equation.
A) for every integer n.
B) for every integer n.
C) for every integer n.
D) for every integer n.
E) for every integer n.

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Q 133Q 133

Find all solutions of the equation.
A) and for every integer n.
B) and for every integer n.
C) and for every integer n.
D) for every integer n.
E) and for every integer n.

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Q 136Q 136

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .
A)
B)
C)
D)
E)

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Q 140Q 140

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.
A)
B)
C)
D)
E)

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Q 147Q 147

Use the graph of f to find the simplest expression g(x) such that the equation f (x) = g (x) is an identity.
A)
B)
C)
D)
E)

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Q 148Q 148

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula where D is the depth (in kilometers) below the surface of the focal point of the earthquake. For the San Francisco earthquake of 1906, S was 4 meters and D was 3.08 kilometers. Approximate M for d = 6 kilometers. Round the answer to the nearest hundredth.
A) m
B) m
C) m
D) m
E) m

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Q 149Q 149

A golfer, centered in a b = 40-yard-wide straight fairway, hits a ball a = 230 yards. Approximate the largest angle the drive can have from the center of the fairway if the ball is to stay in the fairway (see the figure). Round the answer to the nearest hundredth.
A)
B)
C)
D)
E)

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