Question

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 79 degrees and the low temperature of 51 degrees occurs at 4 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t) = 1

Answer 1

Given: 79" max. Temp = min. temp = 51° at 4 am let function is DCD - Acos (BC*-D)] tc C = max temp & min. temp 2 c 79+ St 2. 1 | с 65°

D(4) = stº (4, 5) D116) = 79 D (28) : ) S° (IG, 79° ) (28. $1") period 24 hour 24 hour 25 B (period = 21 2 24 El Amplitude max.temp- mintemp 2 79 -S! 2 Amplitude TAI: 14 cind D - 4 A 06, 19) 79 GS B: 65" 5) (4, SL) (28,51) A: -14

cilver graph is reflection of graph cosine about x-axis A bo 14 Then: D(+) = - 14 cos [A (7-4) ] +65

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