Trigonometry homework help

Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 78 and 92 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 82 degrees?

Answer 1

T(t)=Asin[B(t-C)]+D

A= (92-78)/2= 7

B= 2pi/24=pi/12

c= phase shift=16

D= (92+78)/2=85

85 when t=8

pi/12)(8-C)=2pi

24=8-C

C=16

82= 7sin[(pi/12)(t-16)]+85

solve for t

sin[pi/12)(t-16)= -3/7

(pi/12)(t-16)= sin^-1(-3/7)=-25.38 degrees = -.141pi

(t-6)/12=-.141

t=6+12(.141)

=7.69 hours after midnight

= 7:42 am

or

7:41:30 am