Functions (trigonometric)

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree.  The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse? 

• 7.5 ft 
• 15 ft 
• 26 ft 
• 30 ft 

 $f\left(w\right)\ =\ 55\cos\left(\frac{2\pi}{52}\right)+40$ 

The average temperature in a city can be approximated by the function f where w is the number of weeks.

What is the amplitude and what does it tell us in this context?

• The temperature starts at 40. 
  

• The temperature after 40 weeks.
  

• The median temperature of the city is 40.
  

Tom is riding a Ferris wheel with a radius of 45 meters and a center 51 meters off the ground. Assume Tom starts at the right-hand side of the Ferris wheel and it rotates counter-clockwise. 

Find Tom's height after the wheel rotates  $208^{\circ}$  

• about 78 meters

• about 27 meters

• about -21 meters

• about 30 meters

Kim is riding a Ferris wheel with a diameter of 72 meters and a center 40 meters off the ground. Assume Kim starts at the right-hand side of the Ferris wheel and it rotates counter-clockwise. 

Find Kim's height after the wheel rotates  $407^{\circ}$  

• about 66 meters

• about 26 meters

• about 4 meters

• about -36 meters

The center of a windmill is 20 feet off the ground. The blades extend 4 meters from the center. The windmill rotates counterclockwise. Which equation represents the height of point W as the windmill rotates around?

• h = 4sinθ + 20

• h = -4sinθ + 20

• h = 20sinθ + 4

• h = -20sinθ + 4

The following wave represents a sound recorded for 8s.  Which equation best represents this wave?

• S = 5sin(2x)
• S = sin(5x) 
• S = 5sin(180x)
• S = 180sin(5x)

 $h\left(t\right)\ =\ 275\ +\ 260\sin\left(\frac{2\pi t}{30}\right)$ 

The height in feet of one of the passenger seats on the Ferris wheel can be modeled by the the given function.

What is the DIAMETER of the Ferris wheel?

• 275 feet
  

• 260 feet
  

• 520 feet
  

• 550 feet
  

A Ferris wheel takes 45 seconds to complete one rotation. What is the angular speed of the wheel?

• 45 degrees per second

• 8 degrees per second

• 0.125 degrees per second

• 0.022 degrees per second

The equation represents the height of a passenger on a Ferris wheel (in feet) as a function of time (in seconds)

 $h=85+60\sin\left(7.5t\right)$  
How high off the ground is the passenger if he is at the highest point on the wheel?

• 85 feet

• 60 feet

• 25 feet

• 145 feet

Which graph shows John's height above the round as a function of time as he rides a Ferris wheel?

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