Sinusoidal modeling - the weather

Northern Hemisphere: New York City Southern Hemisphere: Sydney

Data Analysis – Northern Hemisphere

1. After graphing the data on a TI-83 Plus calculator, the graph below was obtained.

Judging from the shape of the graph above, it can be predicted that the data can be modeled by using trigonometric functions (sin or cos).

a. Period: 12 (12 months of the year)

i. Using this value, we can also solve for b, which is 2 ð/p. This calculation gives us a figure of ð/6 as the value for b.

b. Amplitude: 12.45 (half the difference between maximum and minimum temperatures of 24.2 and -.7)

c. Vertical Shift: 11.75 (midpoint of minimum and ma

Looking at the graph, one can deduce that the model used to fit the data should be a trigonometric graph (sin or cos).

As is evident, this model fits the data much better.

d. Phase Shift for sin Graph: 4.25 to the right (indicating that the average of the maximum and minimum temperatures is near the middle of May as it is after 4.25 months, completing April and occurring about a quarter of the way through May)

d. Phase Shift for sin Graph: 10 to the right (indicating that the average of the maximum and minimum temperatures is in the end of October and beginning of December as it is after 10 months).

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