# Math

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The temperature in a certain cave is a sinusoidal function of time. When you first enter the cave, you set up a thermometer to record the temperature. After 19.5 hours, the temperature in the cave is at its maximum: 35 degrees celsius. The temperature then dropped, reaching the minimum temperature of 25 degrees Celesius in 36.5 hours after you entered the cave.
During the first 90 hours after you enter the cave, how much time will the temperature in the cave be above 31 degrees Celsius?

I need help finding the period and the phase shift:
sinusoidal model
T(t)=sin[2pi/B(x-C)]+D

D=(6+5)/2=11/2
A=(6-5)/2=0.5
B=period
C=phase shift

I need help finding B and C

• Math -

Since the max-to-min temperature interval is 17 h, the period is 34 h. Use the time of the maximum to get the phase angle. The argument of the sin function is then pi/2.

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