Question 1

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 18 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (18, 0) and then rotates through an angle of 60^o, what is the new location of the hand?

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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

Sketch the graph of the equation.

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Question 4

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

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Question 5

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 1.86, 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 6

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 25  , and the low temperature of -25  occurs at 4 A.M.

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Question 7

Estimate the horizontal asymptote.

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Question 8

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 9

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 10

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

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Question 11

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 12

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

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Question 13

Find the exact value.

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Question 14

A forester, 200 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 15

Find the period of the equation.

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Question 16

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

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Question 17

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

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Question 18

Find the exact value.

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Question 19

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 20

Find the exact value.

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Quiz 6: The Trigonometric Functions

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

Sketch the graph of the equation.

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

Estimate the horizontal asymptote.

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.

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

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

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

Find the exact value.

A forester, 200 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 the period of the equation.

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

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

Find the exact value.

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.