Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnight and the high and low temperature during the day are 50 and 40 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answer:so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45 Step-by-step explanation:Given data temperature = 45 degreeshigh temperature = 50 degreeslow temperature = 40 degreesto find out an equation for the temperature in terms of tsolutionfirst we find the amplitude i.e.Amplitude (A) = ( high temperature - low temperature )  / 2Amplitude (A) = (50 - 40)  / 2Amplitude (A)  = 5 here we know in a day 24 hours so 2[tex]\pi[/tex] /K = 24K = [tex]\pi[/tex] / 12so we have temperature equation is temperature D = amplitude sinK (t) + avg temperature midnightD = 5 sin [tex]\pi[/tex] / 12 (t) + 45 so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45