Question 1

Find the period of the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the period of the equation. 
A)...

Question 2

Rewrite the expression in nonradical form without using absolute values for the indicated values of  .  ; 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Rewrite the expression in nonradical form without...

Question 3

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

B)

C)

D)

E)

Accepted Answer

The answer of Let P ( t ) be the...

Question 4

Find the exact value. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the exact value. 
A) 
B) 
C)...

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.

A)distance from the bottom of the ladder to the building Ladder 
B)distance from the bottom of the ladder to the Ladder movement

C)distance from the bottom of the ladder to the Ladder movement

D)distance from the bottom of the ladder to the Ladder movement

E)distance from the bottom of the ladder to the Ladder movement

Accepted Answer

The answer of A ladder 26 feet long leans against...

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.
A)31,590 ft
B)10,806 ft
C)3,924 ft
D)31,596 ft
E)3,933 ft

Accepted Answer

The answer of A rocket is fired at sea level...

Question 7

Find the exact value. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the exact value. 
A) 
B) 
C)...

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? A) B) C) D) E)

Accepted Answer

The answer of Points on the terminal sides of angles...

Question 9

Find the exact value. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the exact value. 
A) 
B) 
C)...

Question 10

The graph of an equation of a sine wave is shown in the figure. Find the amplitude, period, and phase shift. 
A)  , 
B)  , 
C)  , 
D)  , 
E)  ,

Accepted Answer

The answer of The graph of an equation of a...

Question 11

Sketch the graph of the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Sketch the graph of the equation. 
A)...

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. A) cm B) cm C) cm D) cm E) cm

Accepted Answer

The answer of The thickness of the ozone layer can...

Question 13

Find an equation using the secant function that has the same graph as  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find an equation using the secant function...

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. 
A)24.2 ft
B)95.7 ft
C)36.8 ft
D)26.8 ft
E)345.6 ft

Accepted Answer

The answer of A CB antenna is located on the...

Question 15

Find y by referring to the graph of the trigonometric function. 
A) 
B) 
C) 
D)1
E)

Accepted Answer

The answer of Find y by referring to the graph...

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.
A)157 mi
B)201 mi
C)270 mi
D)127 mi
E)402 mi

Accepted Answer

The answer of An airplane flying at a speed of...

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.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A builder wishes to construct a ramp...

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.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Scientists sometimes use the formula  to...

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.
A)H = 85%
B)H = 10%
C)H = 55%
D)H = 90%
E)H = 35%

Accepted Answer

The answer of On March 17, 1981, in Tucson, Arizona,...

Question 20

Estimate the horizontal asymptote. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Estimate the horizontal asymptote. 
A) 
B) 
C)...

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.