trigonometry

Question 1

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 210 feet (ft). If the wheel rotates 45° counterclockwise and stops, how much does the height of the seat change?

Answer 1

   2

Question 2

On which interval isy= sin(x) strictly increasing?

Answer 2

(0, pi/2)

Question 3

A waterwheel has a radius of 4 feet, and the center of the wheel is 1 foot under the waterline. You notice a yellow mark at the top of the wheel. If the wheel rotates pi/3radians, how far above the water is the yellow mark?

Answer 3

1 foot

Question 4

Which angle is coterminal to 3pi/4 radians?

Answer 4

• 5pi/4 radians

Question 5

Which expression is equal to –1?

Answer 5

sin (3pi/2)

Question 6

In which quadrant(s) are tan(x) and sin(x)both negative?

Answer 6

quadrant IV

Question 7

Which angle has a terminal side in quadrant III?

Answer 7

579

Question 8

A convertible is traveling at 45 miles per hour, and its wheels have a diameter of 48 inches. How many complete revolutions do the wheels make in one minute?

Answer 8

315

Question 9

A hamster wheel has a diameter of 9 inches and makes one revolution every 3 seconds when the hamster is running on it. From the perspective of the spinning wheel, what is the angular velocity of the hamster in radians per second? Round your answer to the nearest hundredth.

Answer 9

2.09

Question 10

A machine wheel spins at a rate of 500 revolutions per minute. If the wheel has a diameter of 80 centimeters, what is the angular speed of the wheel, in radians per second? Round your answer to the nearest hundredth.

Answer 10

52.36

Question 11

A 40-meter-long blade of a wind turbine makes one complete revolution in 10 seconds. To the nearest tenth, the linear velocity of the blade is ? meters per second.

Answer 11

25.1

Question 12

A particle travels along a circular path that has a radius of 3 feet. The angular velocity of the particle is 18 radians per minute.

The linear velocity of the particle is ? feet per minute.

Answer 12

54

Question 13

Billy goes on the teacup ride at the local carnival. He is seated 16 inches from the center of his teacup, which is spinning at a rate of 4 revolutions per minute. What is Billy’s angular velocity, in radians per second? Round your answer to the nearest hundredth.

Answer 13

0.42

Question 14

Marisol has a bicycle with wheels of 29 inches in diameter. Eliza has a bicycle with wheels of 26 inches in diameter. Both women pedal their bicycles so that the wheels turn at a constant rate of 150 revolutions per minute.

Which statement compares the speeds of the two women? (Note: 1 mile = 5,280 feet)

Answer 14

Marisol travels approximately 1.34 miles per hour faster than Eliza.

Question 15

A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)

Answer 15

21.8

Question 16

Consider the functiony=asin(bx), wherea> 0 andb> 0. Which change compresses the graph vertically?

Answer 16

decrease a

Question 17

which function has a period of 4pi

Answer 17

y = 1/2 sin (1/2 x)

Question 18

Which statement illustrates why cosine is an even function?

Answer 18

cos (- pi/4) = cos (pi/4)

Question 19

If the functiony= sinxis transformed to y = 3sin(2/3 x) ,how do the amplitude and period change?

Answer 19

The amplitude increases, and the period increases.

Question 20

On the interval 0 ≤x≤ 2π, what are thex-intercepts ofy= sinx?

Answer 20

0, π, and 2π

Question 21

What is the equation of a sine function with an amplitude of 2 and a period of 4π?

Answer 21

y = 2sin (1/2 x)

Question 22

Consider the functiony=acos(bx), wherea> 0 andb> 0. Which change affects the locations of thex-intercepts of the graph?

Answer 22

decrease b

Question 23

Suppose the functionf(t) = 95 cos (pi/10 t) + 120 models the height of a seat on a Ferris wheel aftertminutes.

Based on this information, what is the diameter of the Ferris wheel?

Answer 23

190ft