Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 92 degrees occurs at 3 PM and the average temperature for the day is 85 degrees. Find the temperature, to the nearest degree, at 10 AM.

Please provide step by step how to find x after finding equation

Answer 1

since the temperature pattern inil remain same every day so the time period will be 24 hrs. De - l = 2 = 7/12 24 The temperature will ossilate about the neean temperature. So (t=0 at 3pm) T(t) = 85+ A cos a to Since 920 the So highest temp. is 8 st + A =92 or A = 92-85 SO 7 08 t t. I (t) = 85 t 10am t = 19 12 So at so Tet) - 85+ 7 cas iga T = 91.97 » 92 degrees. 12

Step-1 For simplicity, we have assumed the time t to start from 3 Pue. so accordingly to have makinea at 3 pm we took cos function for osselation about mean temp. SO TIE)= 85+ A cos wt Step - 2 Mare temp. is 92% so 85+ A = 92 zs Az7 tu Step-3 every gele will be reapeat itself every day. So T = time period a 24 kls. We 2n = 27 z T24 12 .

so Tit) = 85+ 7 cos t t.