Applying and analysing trigonometric functions

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function:
 $y=19+6\sin\left(\frac{π}{12}(x–11)\right)$   
where y is the temperature (ºC) and x is the time in hours past midnight. What are the minimum and maximum temperatures in the office?

• 13ºC and 25ºC

• 17ºC and 23ºC

• 5ºC and 17ºC

• 8ºC and 30ºC

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Use the equation or table to decide: how often does the tide cycle repeat?

• Once every 3.1 hours.
• Once every 6.2 hours.
• Once every 9.3 hours.
• Once every 12.4 hours.

What is the minimum height on the Ferris wheel?

• 1
• 4
• 7
• 24

• A

• B

• C

• D

Raya is riding a Ferris wheel with a radius of 50 meters and a center 65 meters off the ground. 

Assume Raya starts at the right-hand side of the Ferris wheel and it rotates counter-clockwise. 

Write an equation to model Raya's height at angle $\theta$  (select all that apply)

•  $h=50\sin\left(\theta\right)+65$  

•  $h=65\sin\left(\theta\right)+50$  

•  $h=65+50\sin\left(\theta\right)$  

•  $h=50+65\sin\left(\theta\right)$  

The given equation represents height of a Ferris wheel platform above the ground, in feet, as a function of time, in seconds. Choose all of the statements that are TRUE.

h = 45 + 30sin(7t)

• The radius of the wheel is 30 feet

• The center height of the wheel is 45 feet

• It takes 7 seconds to make one complete rotation

• The center height of the wheel is 30 feet

• The radius of the wheel is 45 feet

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function:

y = 5 sin( π/12 (x – 11)) +18

where y is the temperature (ºC) and x is the time in hours past midnight. What are the minimum and maximum temperatures in the office?

• 12ºC and 23ºC

• 13ºC and 23ºC

• 5ºC and 18ºC

• 11ºC and 23ºC

• min: 13ºC

  max: 25ºC

• min: 17ºC

  max: 23ºC

• min: 5ºC

  max: 17ºC

• min: 8ºC

  max: 30ºC

A 30 ft. wire stretches from the top of a light pole diagonally to the ground. The light pole is 10 feet high. What is the angle the wire makes with the ground?

• 66 degrees
• 80 degrees
• 30 degrees
• 19 degrees