1
$\begingroup$

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.

  • 1
    The rotated version of the sine curve is no longer necessarily a function; it no longer passes the vertical line test in general...2011-11-07
  • 0
    Yes you're right, if my angle were bigger than 45 and my domains were different. That's not the case.2011-11-07

1 Answers 1