Need help with graphing...

Question

I have to make a sin equation for the length of day for a city on Jun 21 the longest day of the year day is 15.36 hours long and on Dec. 21 the shortest day of the year the day light is 9 hours. How would you write a sin equation showing this. I really need help because I have been trying for hours and I can't get what to do.

Answer 1

Try y = A sin(2πt/T - φ) + k

 

 

y: the length of day since midnight Jan 1 in hours

 

A: the difference between the longest and shortest day in hours

 

t: the time in days starting from midnight Jan 1.

 

T: 365.25 days

 

φ: phase shift with respect to midnight Jan 1.

 

k: the shortest day in hours

 

 

Finding the phase shift will be the most challenging.  Good luck!