Modeling with Periodic Functions

Question 1

a =

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6

Question 2

Question 2

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: 0.5; : 4.243

Question 3

a is the length of the bladeheight of the windmillnumber of rotations per minute.

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A: length of the blade

Question 4

Which periodic function, sine or cosine, would be a simpler model for the situation? Explain.

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A cosine function would be a simpler model for the situation. The minimum depth (low tide) occurs at t = 0, so a reflection of the cosine curve has a minimum there. A sine model would require a phase shift, while a cosine model does not.

Question 5

This amplitude is [___] meters. a = [___]

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1.5; -1.5

Question 6

The graph of these points follows a path resembling a .

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C: cosine curve reflected across the x-axis

Question 7

A graph has month on the x-axis and temperature in degrees Fahrenheit on the y-axis. Month 0 is 23; Month 1 is 35; month 2 is 48; month 3 is 65; month 4 is 74; month 5 is 80; month 6 is 76; month 7 is 64; month 8 is 50; month 9 is 32; month 10 is 24; month 11 is 20. Use the graph to write an equation y = acos[b(x – h)] + k to model the situation.The amplitude is ,

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30

Question 8

The blades of the windmill turn on an axis that is 5152025 feet from the ground.

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C: 20

Question 9

On a coordinate plane, a curve starts at (0, 10). It has a maximum of y = 16 and a minimum of y = negative 2.5. On a coordinate plane, a curve starts at (0, 10). It has a maximum of y = 18 and a minimum of y = 4. On a coordinate plane, a curve starts at (0, 10). It has a maximum of y = 15 and a minimum of y = 8. On a coordinate plane, a curve starts at (0, 10). It has a maximum of y = 18 and a minimum of y = 4.

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B:

Question 10

The period is seconds.

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2

Modeling with Periodic Functions Answers

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