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Exam 6: The Trigonometric Functions

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Exam 1: Fundamental Concepts of Algebra150 Questionsadd course
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Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. in degrees and D in meters is given by Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. , where Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. meter, its resolution is Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. . Approximate the diameter of the lens to the nearest hundredth of a meter. Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter.

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Question 41

The popular biorhythm theory uses the graphs of three simple sine functions to make predictions about an individual's physical, emotional, and intellectual potential for a particular day. The graphs are given by The popular biorhythm theory uses the graphs of three simple sine functions to make predictions about an individual's physical, emotional, and intellectual potential for a particular day. The graphs are given by with t in days and t = 0 corresponding to birth. Find the value of b for the physical cycle, which has a period of 29 days. with t in days and t = 0 corresponding to birth. Find the value of b for the physical cycle, which has a period of 29 days.

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Question 42

Find the exact values of the six trigonometric functions of the angle, whenever possible. Find the exact values of the six trigonometric functions of the angle, whenever possible.

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Question 43

Estimate the horizontal asymptote. Estimate the horizontal asymptote.

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Question 44

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 45

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 46

Find the quadrant containing Find the quadrant containing if the given conditions are true. and if the given conditions are true. Find the quadrant containing if the given conditions are true. and and Find the quadrant containing if the given conditions are true. and

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Question 47

Scientists sometimes use the formula Scientists sometimes use the formula to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature of 32 occurs at 2 P.M., and the average temperature of 23 occurs 6 hours later. to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in Scientists sometimes use the formula to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature of 32 occurs at 2 P.M., and the average temperature of 23 occurs 6 hours later. , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature of 32 Scientists sometimes use the formula to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature of 32 occurs at 2 P.M., and the average temperature of 23 occurs 6 hours later. occurs at 2 P.M., and the average temperature of 23 Scientists sometimes use the formula to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature of 32 occurs at 2 P.M., and the average temperature of 23 occurs 6 hours later. occurs 6 hours later.

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Question 48

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

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Question 49

Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. in degrees and D in meters is given by Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. , where Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. meter, its resolution is Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter. . Approximate the diameter of the lens to the nearest hundredth of a meter. Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution ( see the figure ) can be improved by using a lens with a larger diameter D. The relationship between in degrees and D in meters is given by , where is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of meter, its resolution is . Approximate the diameter of the lens to the nearest hundredth of a meter.

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Question 50

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 1.93, 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 1.93, 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 1.93, 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 1.93, I<sub> o </sub>/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter. 1.93, 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 1.93, 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 51

A ship leaves port at 4:00 P.M. and sails in the direction A ship leaves port at 4:00 P.M. and sails in the direction at a rate of 24 mi/hr. Another ship leaves port at 4:30 P.M. and sails in the direction at a rate of 22 mi/hr. Approximately how far apart are the ships at 7:00 P.M.? at a rate of 24 mi/hr. Another ship leaves port at 4:30 P.M. and sails in the direction A ship leaves port at 4:00 P.M. and sails in the direction at a rate of 24 mi/hr. Another ship leaves port at 4:30 P.M. and sails in the direction at a rate of 22 mi/hr. Approximately how far apart are the ships at 7:00 P.M.? at a rate of 22 mi/hr. Approximately how far apart are the ships at 7:00 P.M.?

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Question 52

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 53

As As for some real number . Use a graph to predict . for some real number As for some real number . Use a graph to predict . . Use a graph to predict As for some real number . Use a graph to predict . . As for some real number . Use a graph to predict . As for some real number . Use a graph to predict .

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Question 54

A builder wishes to construct a ramp 26 feet long that rises to a height of 6 feet above level ground. Approximate the angle that the ramp should make with the horizontal. Round the answer to the nearest degree.

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Question 55

Verify the identity by transforming the left-hand side into the right-hand side. Verify the identity by transforming the left-hand side into the right-hand side.

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Question 56

Express the angle as a decimal, to the nearest ten-thousandth of a degree. Express the angle as a decimal, to the nearest ten-thousandth of a degree.

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Question 57

Estimate the horizontal asymptote. Estimate the horizontal asymptote.

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Question 58

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 60<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 60<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 60<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 60<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 60<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 60<sup> o </sup> and the sun is in the southeast? Round the answer to the nearest integer. is equal to 60 o and the sun is in the southeast? Round the answer to the nearest integer.

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Question 59

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 60
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