U(t) Linear Function Question?

Question

On a particular day, a town's electricity usage can be approximated by a sinusoidal function U(t) where t=0 corresponds to midnight. The function has a period of 24 hours and goes from a low of 30,000 kilowatts at 6 A.M. to a high of 60,000 kilowatts at 6 P.M. Write a formula for U(t)

Answer 1

LOL. This can be in sine or cosine... §

I will use U(t) = A sin(kt + b) + H

period: 2π/k = 24 ... k = π/12
since the 6AM is the lowest point, the zeros are on 12 midnight and 12 noon. We can use the 12 midnight as the starting point but that will imply the sine function is negative.

amplitude: [60 - 30] / 2 = 15 , in thousands.

middle: [60+30]/2 = 45 , in thousands.

Thus U(t) = - 15,000 sin(π·t/12) + 45,000. t is in hours.

Answer 2

P= A +B sin(pi/12 t) as w=2pi/T
for t = 6A.M
30,000 = A+B
for t = 6 P.M = 18 h
60,000= A-B
A = 45,000 and B = -15,000
U(t) = 45,000- 15,000 sin (pi/12*t) 0<=t<=24

Answer 3

U(t) is a semi-function of sin-graph...