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Exam 6: The Trigonometric Functions

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Exam 1: Fundamental Concepts of Algebra150 Questionsadd course
Exam 2: Equations and Inequalities142 Questionsadd course
Exam 3: Functions and Graphs147 Questionsadd course
Exam 4: Polynomial and Rational Functions147 Questionsadd course
Exam 5: Inverse, Exponential, and Logarithmic Functions144 Questionsadd course
Exam 6: The Trigonometric Functions150 Questionsadd course
Exam 7: Analytic Trigonometry150 Questionsadd course
Exam 8: Applications of Trigonometry144 Questionsadd course
Exam 9: Systems of Equations and Inequalities147 Questionsadd course
Exam 10: Sequences, Series and Probability150 Questionsadd course
Exam 11: Topics From Analytic Geometry150 Questionsadd course
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Find the exact value. Find the exact value.

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Question 101

Find the amplitude, the period, and the phase shift. Find the amplitude, the period, and the phase shift.

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Question 102

Simplify the expression. Simplify the expression.

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Question 103

Express Express = 2 in terms of degrees, minutes, and seconds, to the nearest second. = 2 in terms of degrees, minutes, and seconds, to the nearest second.

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Question 104

Find the period of the equation. Find the period of the equation.

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Question 105

Approximate the acute angle Approximate the acute angle to the nearest . to the nearest Approximate the acute angle to the nearest . . Approximate the acute angle to the nearest .

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Question 106

Find the exact value. Find the exact value.

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Question 107

A ladder 26 feet long leans against the side of a building, and the angle between the ladder and the building is A ladder 26 feet long leans against the side of a building, and the angle between the ladder and the building is . A. Approximate the distance from the bottom of the ladder to the building. Give the answer to one decimal place. B. If the distance from the bottom of the ladder to the building is increased by 2 feet, approximately how far does the top of the ladder move down the building? Give the answer to one decimal place. . A. Approximate the distance from the bottom of the ladder to the building. Give the answer to one decimal place. B. If the distance from the bottom of the ladder to the building is increased by 2 feet, approximately how far does the top of the ladder move down the building? Give the answer to one decimal place.

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Question 108

Find the exact value. Find the exact value.

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Question 109

The thickness of the ozone layer can be estimated using the formula The thickness of the ozone layer can be estimated using the formula where I<sub> 0 </sub> is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 10<sup> - 8 </sup> centimeter with k 1.86, I<sub> o </sub>/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter. where I 0 is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and The thickness of the ozone layer can be estimated using the formula where I<sub> 0 </sub> is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 10<sup> - 8 </sup> centimeter with k 1.86, I<sub> o </sub>/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter. is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 The thickness of the ozone layer can be estimated using the formula where I<sub> 0 </sub> is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 10<sup> - 8 </sup> centimeter with k 1.86, I<sub> o </sub>/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter. 10 - 8 centimeter with k The thickness of the ozone layer can be estimated using the formula where I<sub> 0 </sub> is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 10<sup> - 8 </sup> centimeter with k 1.86, I<sub> o </sub>/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter. 1.86, I o /I is measured as 1.72 and The thickness of the ozone layer can be estimated using the formula where I<sub> 0 </sub> is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, k is the absorption constant of ozone for that wavelength, and is the acute angle that the sunlight makes with the vertical. Suppose that for a wavelength of 3,055 10<sup> - 8 </sup> centimeter with k 1.86, I<sub> o </sub>/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter. . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.

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Question 110

The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula where R<sub> 0 </sub> is the maximum solar radiation possible, is the angle that the sun makes with the horizontal, and is the direction of the sun in the sky, with = 90<sup> o </sup> when the sun is in the east and = 0 <sup> o </sup> when the sun is in the south. What percentage of R<sub> 0 </sub> is striking the wall when is equal to 30<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. where R 0 is the maximum solar radiation possible, The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula where R<sub> 0 </sub> is the maximum solar radiation possible, is the angle that the sun makes with the horizontal, and is the direction of the sun in the sky, with = 90<sup> o </sup> when the sun is in the east and = 0 <sup> o </sup> when the sun is in the south. What percentage of R<sub> 0 </sub> is striking the wall when is equal to 30<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. is the angle that the sun makes with the horizontal, and The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula where R<sub> 0 </sub> is the maximum solar radiation possible, is the angle that the sun makes with the horizontal, and is the direction of the sun in the sky, with = 90<sup> o </sup> when the sun is in the east and = 0 <sup> o </sup> when the sun is in the south. What percentage of R<sub> 0 </sub> is striking the wall when is equal to 30<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. is the direction of the sun in the sky, with The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula where R<sub> 0 </sub> is the maximum solar radiation possible, is the angle that the sun makes with the horizontal, and is the direction of the sun in the sky, with = 90<sup> o </sup> when the sun is in the east and = 0 <sup> o </sup> when the sun is in the south. What percentage of R<sub> 0 </sub> is striking the wall when is equal to 30<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. = 90 o when the sun is in the east and The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula where R<sub> 0 </sub> is the maximum solar radiation possible, is the angle that the sun makes with the horizontal, and is the direction of the sun in the sky, with = 90<sup> o </sup> when the sun is in the east and = 0 <sup> o </sup> when the sun is in the south. What percentage of R<sub> 0 </sub> is striking the wall when is equal to 30<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. = 0 o when the sun is in the south. What percentage of R 0 is striking the wall when The amount of sunshine illuminating a wall of a building can greatly affect the energy efficiency of the building. The solar radiation striking a vertical wall that faces east is given by the formula where R<sub> 0 </sub> is the maximum solar radiation possible, is the angle that the sun makes with the horizontal, and is the direction of the sun in the sky, with = 90<sup> o </sup> when the sun is in the east and = 0 <sup> o </sup> when the sun is in the south. What percentage of R<sub> 0 </sub> is striking the wall when is equal to 30<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. is equal to 30 o and the sun is in the southeast? Round the answer to the nearest integer.

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Question 111

Find the amplitude, the period, and the phase shift. Find the amplitude, the period, and the phase shift.

(Multiple Choice)
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Question 112

Use the graph of a trigonometric function to aid in sketching the graph of the equation without plotting points. Use the graph of a trigonometric function to aid in sketching the graph of the equation without plotting points.

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Question 113

Refer to the graph of y = cos x to find the separate values of x in the interval Refer to the graph of y = cos x to find the separate values of x in the interval that satisfy the equation. that satisfy the equation. Refer to the graph of y = cos x to find the separate values of x in the interval that satisfy the equation.

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Question 114

Use fundamental identities to find the exact values of the trigonometric functions for the given conditions. Use fundamental identities to find the exact values of the trigonometric functions for the given conditions.

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Question 115

The phases of the moon can be described using the phase angle The phases of the moon can be described using the phase angle , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon: , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, The phases of the moon can be described using the phase angle , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon: changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by The phases of the moon can be described using the phase angle , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon: , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon: The phases of the moon can be described using the phase angle , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon: The phases of the moon can be described using the phase angle , determined by the sun, the moon, and the Earth, as shown in the figure. Because the moon orbits Earth, changes during the course of a month. The area of the region A of the moon, which appears illuminated to an observer on Earth, is given by , where R = 1,080 mi is the radius of the moon. Approximate A for the following position of the moon:

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Question 116

A CB antenna is located on the top of a garage that is 17 feet tall. From a point on level ground that is 120 feet from a point directly below the antenna, the antenna subtends an angle of A CB antenna is located on the top of a garage that is 17 feet tall. From a point on level ground that is 120 feet from a point directly below the antenna, the antenna subtends an angle of , as shown in the figure. Approximate the length of the antenna. Give the answer to one decimal place. , as shown in the figure. Approximate the length of the antenna. Give the answer to one decimal place. A CB antenna is located on the top of a garage that is 17 feet tall. From a point on level ground that is 120 feet from a point directly below the antenna, the antenna subtends an angle of , as shown in the figure. Approximate the length of the antenna. Give the answer to one decimal place.

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Question 117

Points on the terminal sides of angles play an important part in the design of arms for robots. Suppose a robot has a straight arm 20 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (20, 0) and then rotates through an angle of 60 o , what is the new location of the hand?

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Question 118

The graph of an equation of a sine wave is shown in the figure. Find the amplitude, period, and phase shift. The graph of an equation of a sine wave is shown in the figure. Find the amplitude, period, and phase shift.

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Question 119

Points on the terminal sides of angles play an important part in the design of arms for robots. Suppose a robot has a straight arm 20 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (20, 0) and then rotates through an angle of 60 o , what is the new location of the hand?

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Question 120
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