Functions (trigonometric)

Say 'TRUE' or 'FALSE'
If both the height of the pole and the distance of the point of observation from the foot are increased by the same length, the angle of elevation of its top remains unchanged

• TRUE
• FALSE

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

 $h=58+33\sin\left(6t\right)$  
How many seconds does it take the wheel to rotate 315 degrees?

• 180 seconds

• 7.5 seconds

• 52.5 seconds

• 0.019 seconds

The angle of elevation of the top of a cell tower from a point 225 feet away from the base of the tower on flat ground is 37 degrees. What is the height of the cell tower?

• The height of the cell tower is 169.55 feet.

• The height of the cell tower is 291.81 feet.

• The height of the cell tower is 173.99 feet.

• The height of the cell tower is 225.21 feet.

Answer explanation

Tan(37 degrees) = h/225

225(Tan(37 degrees)) = h

H = 169.55

The maximum daily temperature is $34\degree c$   and the minimum temperature is $27\degree c$  in June, calculate the amplitude.

• 3.5

• 30.5

• 4.5

• 30

The temperature is degrees fahrenheit at a given location goes though a similar cycle each day. The low of 30 degrees occurs at 6:00 am. The high is 70 degrees at 6pm. What equation models the temp as a function of time hours since noon (12pm).

• $f\left(t\right)=\ 20\sin\left(\frac{\pi}{12}x\right)+50$

• $f\left(t\right)=20\left(\frac{\pi}{6}x\right)+50$

• $f\left(t\right)=\ -20\sin\left(\frac{\pi}{12}x\right)+50$

• $f\left(t\right)=-20\sin\left(\frac{\pi}{6}x\right)+50$

Jordan is stuck at the top of a Ferris wheel. Her mother is standing 38 feet from the base of the wheel watching her. If the angle of elevation from Jordan's mom to Jordan is 73^o, how far off the ground is Jordan?

• 118.2 ft

• 120.9 ft

• 124.3 ft

• 126.5 ft

In St. Louis, MO, the longest day is July 1, with 14:45 of daylight. The shortest day is January 1st, with 9:45 of daylight. If construct a graph of daylight over the course of the year, from April 1 to March 31, the equation of the graph would be

• y= 300sin(pi/6 x) + 735

• y= 300cos(pi/6 x) + 735

• y= 150sin(pi/6 x) + 735

• y= -150cos(pi/6 x) + 735

• y= -300cos(pi/6 x) + 735

The equation y = 15sin(2π t / 3) represents the vertical position of Luna, in feet, as she spins around on a merry-go-round in t seconds.

How long does it take the merry-go-round to complete one full revolution?

• 3 seconds

• 15 seconds

• 2/3 second

• 6 seconds

The angle of elevation of the top of a tower is 30°.  If the height of the tower is doubled then the angle of elevation of the top will be_____

• No change: 30°
• Will be doubled : 60°
• will become 45°
• None of the above

The data table in the picture shows the average length of daylight for each month of the year.  Calculate the sinusoidal regression equation of the data.

• y = 2.69sin(0.512x - 1.47) + 11.89
• y = 11.89sin(2.69x + 0.512) - 1.47
• y = -0.106x + 12.44
• y = 12.44x - 0.106