I want to be able to directly use the resulting function of rotating a sine function.
My original function is:
f(x) = B * sin(x)
My domain for x is -pi to pi.
My domain for B is -1 to 1.
When I rotate it by theta degrees I have (actually my theta is fixed and is 45 degrees):
x' = cos(theta) * x - sin(theta) * B * sin(x) y' = sin(theta) * x + cos(theta) * B * cos(x)
The problem is now I have a new function depending on x but that has at its source x' and not x anymore. That's not what I need.
If I try to substitute x in the y' function I end up not being able to use my previous x because I can not solve it in a closed form.
Am I missing something here? Is there any mathematical trick to do this job? I have already tried parametric equations to no avail.