Thread: General Sine Function question - need help to find "C"

the question is that i have to fit a general sine model (AsinB(x-C)+D) from some data without using technology
the table is as follows (this is a table about temperatures)
jan feb mar apr may jun july aug sept oct nov dec
15, 16, 14.5, 12, 10, 7.5, 7, 7.5, 8.5, 10.5, 12.5, 14

so far i have managed to get y=5.5sin(pi/6)(x-C)+22.5 but the textbook doesn't quite explain exactly how to find "C" without having a graph already drawn. the correct answer is y=5.5sin(pi/6)(x-10.7)+22.5.

Any help on this asap would be greatly appreciated

You've left a lot out! What is "x"?? I assume your "y" is the temperature but the independent variable is the names of months. Are you taking jan= 1, feb= 2, etc.? If so then you need to remember that standard "sin(x)" starts one period at x= 0 with sin(0)= 0, exactly half way between the maximum sine value of 1 and the minimum sine value of -1. What is your maximum temperature? What is you minimum temperature? What month has a value halfway between? You will want "C" to correspond to that month so that x- C= 0 for that month.

But how did you, and your textbook, get that "22.5"? Since the largest sine can be is 1 and the lowest is -1, whatever, C is, 5.5sin(pi/6(x- C)+ 22.5 has a smallest possible value of -5.5+ 22.5= 17 and a largest possible value of 5.5+ 22.5= 28. NONE of the temperatures you gives are in that interval! I am also wondering why your "temperature" chart gives a low temperature for july. Are you in the southern hemisphere?

yeah sorry, i checked with my teacher and it was in fact a text book mistake. the entire page was wrong apparently. thanks for trying to help anyway