TEMPERATURE During a summer day the ground temperature at a

TEMPERATURE During a summer day, the ground temperature at a desert location was recorded and graphed as a function of time, as shown in the following figure. The graph can be approximated by f(t) = A cos (bt + c) + d. Find the equation and approximate the temperature (to the nearest degree) at 1:00 RM.

Solution

Period = 9 - (-15) = 24 hrs

b = 2pi/24 = pi/12

A +d = 120

d - A= 60

--------- 2d = 180 ; d = 90

A = 30

So, f(t) = 30cos(pi*x/12 +c) +90

at x= 9 ; f(t) = 120

120 = 30cos(pi*9/12 +c) + 90

1 = cos(3pi/4 +c)

3pi/4 +c =0 ; c= -3pi/4

So, f(t) = 30cos(pi*x/12 -3pi/4) +90

at t = 7 hrs

f(7) = 30cos(7pi/12 - 3pi/4) + 90

= 30cos(-2pi/4) +90

= 90 deg