SOLUTION: Help with this Please! Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 67 degrees at midnight and the high and low te

Algebra ->  Human-and-algebraic-language -> SOLUTION: Help with this Please! Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 67 degrees at midnight and the high and low te      Log On


   

Question 1179525: Help with this Please!
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 67 degrees at midnight and the high and low temperature during the day are 76 and 58 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
D(t)= ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
67 degrees at midnight
during the day are 76 and 58 degrees
find an equation for the temperature,
D%28t%29=a%2Asin%28b%28t-d%29%29%2Bc
the average is:
76-67=9
67-58=9
amplitude (a) is 9;
period = 24 hours;
Assuming t is the number of hours since midnight when the temperature is falling amplitude a have negative sign

a=-9
b=2pi%2F24=%281%2F12%29pi
c=67
d=0
D%28t%29=-9sin%28%281%2F12%29pi%2At%29%2B67