Answer:
L =
376.5sin[(2πx/365)-(168 ×2π/365)] +720
Step-by-step explanation: Given that
Number of days = 365
Then each day must be 2π /365 rads
The midline is in minutes = 12 × 60 = 720 minutes
Amplitude = 1096.5 - 720 = 376.5
Let use the sine function
Let January 1st = "Day 0"
that is, where t = 0
Using the basic function
L = 376.5 sin [ ( 2πt/ 365 ) ]
The shortest day of the year is half a year later, and it's 382.5 minutes long. Which is on December 21
Then, we need to find the phase shift
The phase shift equation is
ps = 360 × td / p,
where ps is the phase shift in degrees, td is the time difference between waves and p is the wave period.
td = 720 - 382.5 = 337.5
Ps = (360 × 337.5)/720 = 168.75
So, the phase shift can be expressed as 168 × 2π/ 365
Therefore, function L can be expressed as L =
376.5sin[(2πx/365)-(168 ×2π/365)] +720