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The data in the table shows a sinusoidal relationship between the number of seconds an object has been moving and its velocity v(x), measured in centimeters per second.

 

x 10 20 30 40 50 60 70 80 90 100 110 120
v(x) 65.9 49.9 30.1 14.1 8 14.1 30.1 49.9 65.9 72 65.9 49.9

 

What is true of the cosine function that models the data in the table?

The period of the cosine function is ______ . The equation of the midline of the cosine function is y =_____. The amplitude of the cosine function is ____

 Mar 6, 2020
 #1
avatar+25917 
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Plot all of those points......   then bring the graph back here and we can help you further......     cheeky

 Mar 7, 2020
 #2
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I plotted the points ---> https://www.desmos.com/calculator/gkrhzfgh4l

Guest Mar 7, 2020
 #3
avatar+25917 
+1

Ok...thanx for that !   This looks like a cosine function doesn't it? 

BUT it is taller than a normal cosine function....usually the height of the wave goes from -1 to 1       which means amplitude is 1

    THIS wave goes from 8 to 72      so amplitude is   32     ( 1/2 of the height is amplitude)

 

32 cos x        so far

  Now,     note that the wave is shifted UP from it's normal midline of zero..... the midline of this wave is 40

32 cos x       + 40

 

The period is the amount of x axis this wave takes to make a complete cycle.....  Looks to be 100 seconds

32 cos (x pi/50)   + 40  

 

Check this out......I superimposed the above wave on YOUR graph !

 

https://www.desmos.com/calculator/ozfmq36yob

 

cheeky

ElectricPavlov  Mar 7, 2020

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