Task: 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:
y = f(x) = A sin(Bx-C) + D or y =A cos(Bx-c) + D
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".
NOTE: Here are some examples to make sure you understand how x is to be defined:
Example 1: Then x = 0.25 would be 6:00 am on Jan 1, 2016.
Example 2: Then x = 4.5 would be 12:00 pm (noon) on Jan 5, 2016.
Example 3: Then x = 63.75 would be 6:00 pm on March 4, 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 .
For both Functions: The time zone we will use is our local Atlantic Standard Time (AST).
You will need to research to accurately find the following:
(1) The exact (to the minute) Atlantic Standardtime of the summer solstice in 2016.
i) Use this information to calculate the value of your input variable at that time (round to 3 decimal places). (If you use Cosine, then this will tell you the phase shift.)
ii) Both of your functions will reach their maximum output value at this time.
(2) The exact (to the minute) Atlantic Standardtime of the winter solstice in 2016.
i) Use this information to calculate the value of your input variable at that time (round to 3 decimal places).
ii) Both of your functions will reach their minimum output value at this time.
(3) The length of a year (round to 3 decimal places) in days. This will tell you the period. 365.25
For the Latitude Function: You will need to find the following
(1) The latitude of the Tropic of Cancer (round to 3 decimal places). This will tell you the maximum output (latitude) for your function. 23.437
(2) The latitude of the Tropic of Capricorn (round to 3 decimal places). This will tell you the minimum output (latitude) for your function. (Use negative numbers for southern latitudes.) -23.437
(3) The latitude of the equator. This will tell you the centerline. 0
For the Length of Day Function: You will need to find the following
(1) A city or small island location of your choosing, and its latitude. In your report you must tell me what location you have chosen. St John 18.337
(2) The length of day (sunrise to sunset, in hours and minutes) on the summer solstice at your chosen location. Change this time to hours only (rounded to two decimal places), instead of hours and minutes. This will tell you the maximum output (length of day) for your function.
(3) The length of day (sunrise to sunset, in hours and minutes) on the winter solstice at your chosen location. Change this time to hours only (rounded to two decimal places), instead of hours and minutes. This will tell you the minimum output (length of day) for your function.
(3) Use the information from parts (2) and (3) to calculate the amplitude and the centerline (both rounded to two decimal places).
A few notes about what kind of report I am expecting
Your report must be typed and grammatically correct (this includes spelling and use of notation). You do not have to write long explanations, but you do need to provide the following information in a fashion that is easy to read.
1) State the definition, including units, of all of your variables (even if that means copying parts of what I wrote in this document).
2) Provide the research data (times, dates, latitudes, lengths of day, etc.) upon which your functions are based.
3) Provide the equations for your functions. You will be creating two functions. Use different names for them. Clearly state which function is which
4) State the location that you have chosen, and provide the latitude of the location (you will use this information for part 2 of your project).
Attachment:- Assignment.rar