Question 1

Find the period of the equation.

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Question 2

Rewrite the expression in nonradical form without using absolute values for the indicated values of  .  ;

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Question 3

Let P ( t ) be the point on the unit circle U that corresponds to t. If P ( t ) has the coordinates  , find  ,  ,  ,  .

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Question 4

Find the exact value.

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Question 5

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.

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Question 6

A rocket is fired at sea level and climbs at a constant angle of  through a distance of 11,500 feet. Approximate its altitude to the nearest foot.

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Question 7

Find the exact value.

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Question 8

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 16 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (16, 0) and then rotates through an angle of 60^o, what is the new location of the hand?

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Question 9

Find the exact value.

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Question 10

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 11

Sketch the graph of the equation.

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Question 12

The thickness of the ozone layer can be estimated using the formula where I₀ 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^{- 8} centimeter with k 1.93, I_o/I is measured as 1.72 and . Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.

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Question 13

Find an equation using the secant function that has the same graph as  .

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Question 14

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 15

Find y by referring to the graph of the trigonometric function.

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Question 16

An airplane flying at a speed of 360 mi/hr flies from a point A in the direction  for 15 minutes and then flies in the direction  for 30 minutes. Approximate, to the nearest mile, the distance from the airplane to A.

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Question 17

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 18

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 is 17  , and the low temperature of -17  occurs at 4 A.M.

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Question 19

On March 17, 1981, in Tucson, Arizona, the temperature in degrees Fahrenheit could be described by the equation  while the relative humidity in percent could be expressed by  where t is in hours and t = 0 corresponds to 6 AM. Find the maximum value of the humidity.

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Question 20

Estimate the horizontal asymptote.

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Quiz 6: The Trigonometric Functions

Find the period of the equation.

Rewrite the expression in nonradical form without using absolute values for the indicated values of . ;

Let P ( t ) be the point on the unit circle U that corresponds to t. If P ( t ) has the coordinates , find , , , .

Find the exact value.

A rocket is fired at sea level and climbs at a constant angle of through a distance of 11,500 feet. Approximate its altitude to the nearest foot.

Find the exact value.

Find the exact value.

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

Sketch the graph of the equation.

Find an equation using the secant function that has the same graph as .

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.

Find y by referring to the graph of the trigonometric function.

An airplane flying at a speed of 360 mi/hr flies from a point A in the direction for 15 minutes and then flies in the direction for 30 minutes. Approximate, to the nearest mile, the distance from the airplane to A.

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.

On March 17, 1981, in Tucson, Arizona, the temperature in degrees Fahrenheit could be described by the equation while the relative humidity in percent could be expressed by where t is in hours and t = 0 corresponds to 6 AM. Find the maximum value of the humidity.

Estimate the horizontal asymptote.