## The outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 68°F at

Question

The outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the
temperature is 68°F at midnight and the high and low temperatures during the day are 80°F and 56°F, respectively.
Assuming t is the number of hours since midnight, nd a function for the temperature, D, in terms of t.

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3 months 2022-02-17T20:03:48+00:00 1 Answer 0 views 0

D= – 12sin(π/12)(t) + 68

Step-by-step explanation:

Let temperature D in terms of number of hours t be given as:

D= asinkt + 68

Now,

The difference between high and low temperatures is= 80-56= 24 °F

The period is= 24 hours

So, we have 2π/k= 24

Or, k= 24/2π

Now,

Let a= 12 hours

So, our equation becomes

D= 12sin(2π/24)(t) + 68

This is valid for 12 hours gap. If we want to implement for whole day then

D= – 12sin(π/12)(t) + 68

Put t=0

D= 68°F which is temperature at midnight

Put t=6

D= -12(1)+68

D= 56°F

Put t=18

D= -12(-1) + 68

D= 80°F