A CITY The longest sunlight day is 154626 The shortest sunli

A CITY

The longest sunlight day is 15:46:26

The shortest sunlight day is 8:42:55

Use the information that you found in(a) to create a macthematical model of the form.

h(t) = a sin (bt + c) + d

And the function assume that t=0 starts at midnight between Dece 31 and Jan 1.

Where a,b,c and d are constants that you need to determine, If t is time in days and h is the number of sunlight on day t.

Then a, b,c and d stand for what?

What about the inverse function can do?

d is mid value for the given sine function h(t)

=> d = ( (8:42:55) + (15:46:26) )/ 2 = 12:14:41

a is the maximum difference from the mean value

=> a = ( 12:14:41 - 8:42:55 ) = 3:31:45

b denotes the time period factor . Since cycle of 365 days is equivalent to 2 cycle of sine function

=> b = 2/365

Since , the data provided does not mention the date of longest and shortest daylight , constant c cannot be calculated.

The inverse function of the h(t) would help in predicting the date of the year with the help of the given sunlight data