# Trig

The average monthly temperatures of Atlanta, GA are shown below.
Jan 32 degrees
Feb 35 degrees
Mar 44 degrees
Apr 53 degrees
May 63 degrees
June 73 degrees
July 77 degrees
Aug 76 degrees
Sept 69 degrees
Oct 57 degrees
Nov 47 degrees
Dec 37 degrees
Determine the amplitude, period, phase shift, and vertical shift of a sinusoidal function that models the monthly temperatures using x = 1 to represent January.

Write an equation of a sinusoidal function that models the monthly temperatures.

According to your model, what is Atlanta’s average temperature in July? December?

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1. ok, one more. Then you really must provide some work.
You have
min = 32, max = 77
amplitude = (max-min)/2 = 45/2
center line = (max+min)/2 = 109/2
So far, you have
y = 45/2 sinx + 109/2
The period is clearly 12 months, so since sin(kx) has period 2π/k, we have
2π/k = 12
h = π/6
Now we are down to
y = 45/2 sin(π/6 (x-h)) + 109/2
Now we just need the phase shift. Since cosx has a maximum at x=0, and your graph has a maximum at x=7,
y = 45/2 cos(π/6 (x-7)) + 109/2

Now just plug in your month number to see how closely it fits the table.

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