precalculus homework college

Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 48 and 62 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 50 degrees?

= hours

help please

Answer 1

Since the temp varied between 62 and 48, that is for max to min that is twice the amplitude therefore 62-48=14. Since this is twice A, A=7. The period is 24 hours(one-full day/night) Thus, B=2pi/24= pi/12. Now, at last handle the phase shift. The average temp occurs when t=8(8AM). If it is in phase, it should occurs at t=12. so the phase shift is -4 because 12-8=4, We need that to be zero(middle) at t=0, thus use a sine function. y=7sin(pi/12(t+4)). Now, when is the temp 50 ? (hint y=50)