You need to come up with two related, but different sinusoidal function. You can choose to use sine or cosine. Recall that the forms are:
For both functions: Your input variable (I suggest using x) should be chosen to representrepresents the day of the year (with x = 0 being midnight b/w Dec 31, 2015, and Jan 1, 2016). Another way to say this is that “x is the time, in days, since the start of 2016”.
For Function #1 – The Latitude Function: The output for this function should be chosen to be the latitude of the sun at time x .
For Function #2 – The Length of Day Function: The output for this function should be chosen to be the length of day (sunrise to sunset) at a city or small island location of your choice on the day corresponding to time x .