Question

Over a 24 hour period the temperature in a town can be modeled by one period of a sinusoidal function. The temperature measures 70*F in the morning, rises to a high of 80*F, falls to a low of 60*F, and then rises to 70*F by the next morning.

What is the equation for the sine function f(x), where x represents time on hours since the beginning of the 24 hour period that models the situation​

Answer 1

Start with an initial temperature of T0 = 70° at t = 0 hours, and add to that a sine function that does the following, in order:

Rises by 10°, reaching 80° after 6 hours

Drops by 10º, reaching 70° after 12 hours

Drops by 10°, reaching 60° after 18 hours

Rises by 10°, reaching 70° after 24 hours

Note that the amplitude of the sine function is A = 10°.

T = period of the sine function

T = 24 hours

f(x) = T0 + A sin[(2π/T)x]

where

T0 = 70°

A = 10°

T = 24 hours

x = elapsed time in hours

f(x) = 70º + (10°)sin[(π/12)x]

with x in hours.

Test this solution and see that it fits the data. (Make sure your calculator is in the radian mode!)

Answer 2

10sin(πx/12)+70

Explanation:

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