choosing the parameters

Many calendars number the days of the year. January 1st gets number one, january 2nd gets number 2, january 31st gets 31, february 1st gets 32, december 31st gets 365 in a non-leap year, etc. mary ann noticed that on the northern hemisphere island where she lived there was 14 hours, 42 minutes of sunlight on the longest day of the year and 9 hours, 18 minutes on the shortest. created a sin function or cosine function that would allow someone to input the day number and get the hours of sunlight. explain your reasoning for choosing the parameters that you have.(Headbang)

Northern Hemisphere.

Longest = Summer Solstice = June 21ish
Shortest = Winter Solstice = December 20ish
Middle-est = Vernal Equinox = March 21ish
Other Middle-est = Autumnal Equinox = September 21ish

Where is sin(x) the Greatest? The Least? Middle? What is the period of sin(x)? What is it's amplitude?

Compare y = sin(x) with y = A + sin(x)

Compare y = sin(x) with y = sin(x - B)

Compare y = sin(x) with y = C*sin(x)

Compare y = sin(x) with y = sin(D*x)