Unformatted text preview: Suppose we are given the formula 2π T = 75 + 20 (x − 101) to approximate the average daily temperature 365 in degrees Fahrenheit in Gainesville on day x (x = 1 represents January 1st). We would like to use this formula to
determine the days of the year that the temperature would be 85° F .
We will first determine the answer graphically as follows. Enter the following formulas into your calculator and
draw the graph using [0, 400] for the xsettings and [0,100] for the ysettings. You should see the following
graph. 2π y1 = 75 + 20 (x − 101) 365 y 2 = 85
The graph tells us that the average daily temperature
is 85° F on days 131 and 253. In a nonleap year,
these days would be May 11th and September 10th.
Now let’s solve this equation algebraically. 2 π (x − 101) = 85 365 75 + 20 sin 2π (x − 101) = 10 365 20 sin 2π (x − 101) = 0.5 365 sin Let A = 2π (x − 101) 365
π
sin A = 0.5 → A = ( ≈ 0.52) or A =
6 5π ( ≈ 2.62) 6 Solve the equation A = 2π (x − 101) for x. 365
A= 2π (x − 101) → x − 101 = 365
x= 365 365 (A) 2π
(A) + 101 Substitute in the computed values for A. 2π
x= 365 (0.52) + 101 ≈ 131 → May 11 th 2π
x= 365
2π (2.62) + 101 ≈ 253 → September 10 th ...
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 Fall '09
 COHEN
 Trigonometry, Expression, Fahrenheit, Celsius, 85°, Average daily temperature

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