Question 1

A forester, 210 feet from the base of a redwood tree, observes that the angle between the ground and the top of the tree is  . Estimate the height of the tree.

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Question 2

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 3

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

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Question 4

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 5

Find the exact value.

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...

Question 6

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 7

A builder wishes to construct a ramp 22 feet long that rises to a height of 5.5 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 8

An airplane flying at a speed of 300 mi/hr flies from a point A in the direction  for 30 minutes and then flies in the direction  for 15 minutes. Approximate, to the nearest mile, the distance from the airplane to A.

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Question 9

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

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Question 10

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 11

Find the exact value.

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...

Question 12

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

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Question 13

Find the exact value.

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...

Question 14

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 15

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

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Question 16

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 17

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

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Question 18

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 19

A ladder 18 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 20

A rocket is fired at sea level and climbs at a constant angle of  through a distance of 10,500 feet. Approximate its altitude to the nearest foot.

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Quiz 6: The Trigonometric Functions

A forester, 210 feet from the base of a redwood tree, observes that the angle between the ground and the top of the tree is . Estimate the height of the tree.

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

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 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.

A builder wishes to construct a ramp 22 feet long that rises to a height of 5.5 feet above level ground. Approximate the angle that the ramp should make with the horizontal. Round the answer to the nearest degree.

An airplane flying at a speed of 300 mi/hr flies from a point A in the direction for 30 minutes and then flies in the direction for 15 minutes. Approximate, to the nearest mile, the distance from the airplane to A.

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

Find the exact value.

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

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.

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

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.

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

A rocket is fired at sea level and climbs at a constant angle of through a distance of 10,500 feet. Approximate its altitude to the nearest foot.