Quote:
Oh, that's complicated to describe only with words without showing it on a graph, but I'll try it:
I did it in 4 steps:
1) make the period 23 (i.e. b=?) ==> y = f(x) = a*sin(2*pi/23*x)
2) shift the function upwards, so that y is negative only in an interval of 2.5 (i.e. d=?):
this 2.5 interval is symmetric around the minimum at x=23/4*3 (or the maximum at x=23/4), so this shift-value d is f(23/4-2.5/2) (I took it at the maximum for getting smaller numbers) which leads to d = a*sin(2*pi/23*(23/4-2.5/2)) = a*sin(9*pi/23)
Now we have y = f(x) = a*sin(2*pi/23*x) + a*sin(9*pi/23)
3) now scale the function to get a max. y-value of 1 (i.e. a=?):
you get this max. y-value of 1 for x=23/4:
f(23/4) = a*sin(2*pi/23*23/4) + a*sin(9*pi/23) = a*sin(pi/2) + a*sin(9*pi/23) =
a + a*sin(9*pi/23) = a*(1+sin(9*pi/23)) = 1 ==>
a = 1/(1+sin(9*pi/23))
4) and finally shift the function in x-direction, so that the first zero should be at x=16.5 (i.e. c=?):
as I explained in point 2) the zero of the up-shifted function is currently at 16 (that is 23/4*3-2.5/2), so the function must be shifted to the right by a value of 0.5, and thus x has to be replaced by x-1/2
These 4 steps together lead to the following solution:
y = f(x) = 1/(1+sin(9*pi/23))*[sin(2*pi/23*(x-1/2)) + sin(9*pi/23)]
Franz