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 ____

Guest Mar 6, 2020

#1**+1 **

Plot all of those points...... then bring the graph back here and we can help you further......

ElectricPavlov Mar 7, 2020

#3**+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

ElectricPavlov
Mar 7, 2020