Question

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 89 degrees and the low temperature of 71 degrees occurs at 6 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t) =

Answer 1

jj low high temp temp 719 89 II - at mid right, t=0. mid night temp Fi +89 2 80° - so, at t=0 D=80° C = 80° {from.co * Let the function is, Do aisin (bt) + c 00 a = 89°- 9 2

1) f low temp high temp =899 -> Let the function is, D = a sincbt) + (0 at mid night tao, 2 mid night temp is, high tempt low temp 2 ggº + 71 2 = 80° t =0 -> at D = 80°

şferom Eano → a= high temp-loce temp 2 a = 89° - = 9 2 we know that the Period is 24 his 24 8. 21 h = b EN T 12 » temp after midnight

would decrease, whereas our function has it incresing to 89° when t = 6 (6:am) D = -a sin (bt) + c ED= -9 sin ( t) + 80