General Sine Function

[jackieloaa]

How would I go about modeling a sine equation if i have only coordinates.

The coordinates i have are
Line 1: (-4.5, 1)
(0, 1)
(4, 6.25)
(5.5, 5)


Line 2:
(-4.75, 3)
(1, 1)
(3, 2.5)
(5, 1.25)

 

[chrisr]

The Sinewave has amplitude, period, offset and phase shift.
It's amplitude is it's height above 0 if it had no offset.

So, assuming you want to generate a sine function without using software,
you are looking for y=f(x)=aSin(bx+c)+d,
where a=amplitude, b=period, c=phase shift, d=offset.

You have 4 unknowns and you have offered 4 sets of co-ordinates for each wave.
As Sine is non-linear, we cannot write 4 sets of linear simultaneous equations.

For line1;
f(0)=1, so aSin(c)+d=1.
f(4)=6.25, so aSin(4b+c)+d=6.25.
f(-4.5)=1, so aSin(-4.5b+c)+d=aSin(c)+d, so Sin(-4.5b+c)=Sinc, but these points do not need be a period apart to be equal.
f(5.5)=5, so aSin(5.5b+c)=d=5.

Without knowing some parameter,
it looks like software is needed.