Question

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

What is true of the cosine function that models the data in the table?
Drag a value into each box to correctly complete the statements.

The period of the cosine function is The equation of the midline of the cosine function is y = 20 The amplitude of the cosine function is ​

Answer 1

The period is the change in x required for the function to return to the same value, changing in the same direction. The first two table entries are v(x) = 41.7 and 35.7. The next time that sequence appears is when x=44, so the period is ...

period = 44 -4 = 40 . . . seconds

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The minimum table value is 20; the maximum is 44, so the midline of the function is their average:

midline = (20 +44)/2 = 32

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The amplitude is the maximum deviation from the midline, so is ...

amplitude = 44 -32 = 12

Explanation: