Modeling Trig Functions

What is the period of the function shown in the given graph?

• 7

• 8

• 15

• 16

Find the best equation for the graph shown.

• $y=7\cos\left(\frac{\pi}{8}\left(x-11\right)\right)+12.5$

• $y=7\sin\left(\frac{\pi}{8}\left(x-7\right)\right)+12.5$

• $y=-7\cos\left(\frac{\pi}{8}\left(x-1\right)\right)+12.5$

• $y=-7\sin\left(\frac{\pi}{8}\left(x+1\right)\right)+12.5$

The average person’s blood pressure is modelled by the function f(t)=20sin(160πt)+100,

where f(t) represents the blood pressure at time t measured in minutes.

What is the blood pressure at t=0.07 minute?

• 111.525

• 88.244

• 100

• 120

The average daily high temperature (in celcius) in Karachi, Pakistan, on the t-th day of the year is approximately modelled by
 $T\left(t\right)=29-5\cos\left(\frac{2\pi\left(t-12\right)}{365}\right)$ .  

Find the highest average daily highs in Karachi. Give exact answer.

• -5

• 24

• 29

• 34

The daily temperature in the month of March in a certain city varies from a low of 24°F to a high of 40°F. The temperature reaches the freezing point 32°F at noon and midnight.

Find a sinusoidal function to model daily temperature. Let t=0 correspond to noon.

• $y=8\cos\left(\frac{\pi}{12}x\right)+32$

• $y=8\sin\left(\frac{\pi}{12}x\right)+32$

• $y=8\sin\left(\frac{\pi}{6}x\right)+32$

• $y=-8\cos\left(\frac{\pi}{6}x\right)+32$

The hour hand of the large clock on the wall in Union Station measures 24 inches in length.

At noon, the tip of the hour hand is 30 inches from the ceiling. At 3 PM, the tip is 54 inches from the ceiling, and at 6 PM, 78 inches. At 9 PM, it is again 54 inches from the ceiling, and so forth.

Let y equal the distance from the tip of the hour hand to the ceiling and x be the number of hours after noon.

Find the equation that models the motion of the hour hand.

• 
  

  $y=-24\cos\left(\frac{\pi}{6}x\right)+54$
  

• $y=30\cos\left(\frac{\pi}{6}x\right)+54$

• $y=30\sin\left(\frac{\pi}{6}x\right)+54$

• $y=24\sin\left(\frac{\pi}{6}x\right)+54$

A pendulum swinging next to a wall. The distance from the bob of the pendulum to the wall varies in a periodic way that can be modelled by a sinusoidal function.

The modelling function has a period 0.8 seconds, amplitude 6 cm, and midline at 15 cm. At time t=0.2 , the bob is at its midline, moving towards the wall.

Find the equation of the trig function that models the distance H between the bob and the wall after t seconds.

• $H\left(t\right)=6\sin\left(\frac{5\pi}{2}\left(t+0.2\right)\right)+15$

• $H\left(t\right)=-6\sin\left(\frac{5\pi}{2}\left(t-0.2\right)\right)+15$

• $H\left(t\right)=6\sin\left(\frac{5\pi}{2}t\right)+15$

• 
  

  $H\left(t\right)=-6\cos\left(\frac{5\pi}{2}t\right)+15$