I forgot what the formula for this is.

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In summary: Common_rotationsIn summary, the conversation discusses the concept of rotating a function about the x-axis by a certain angle, and suggests using a rotation matrix to achieve this. The idea is compared to Euler's formula, but it is noted that this formula only applies to complex numbers. The conversation concludes by discussing the difficulties in rotating a function and the possibility of using a 3-dimensional function to achieve this rotation.
  • #1
flyingpig
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If I give you a function f(x) (cartesian) and I ask you to rotate it about the x-axis (counterclockwise) by an angle phi, what is the new function formula?

I remember I did this with matrices, but I can't remember the one for functions. For convenience, let angle phi be 0, pi/2, 3pi/2, and 2pi.

I am guessing 0 would remain the same. I just don't know how to use matrices on functions.

Does anyone understand my question?
 
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  • #3
There's obviously [itex]SO(n)[/itex] but that's matrices.

Doesn't Euler's formula do that same thing?

[itex]e^{i\theta} = cos\theta + isin\theta[/itex]

EDIT: Euler's formula is only for complex numbers.
 
  • #4
Yes, but for functions. Is there no equivalence? I kinda had something like this for conics
 
  • #5
Kevin_Axion said:
There's obviously [itex]SO(n)[/itex] but that's matrices.

Doesn't Euler's formula do that same thing?

[itex]e^{i\theta} = cos\theta + isin\theta[/itex]

EDIT: Euler's formula is only for complex numbers.

No real numbers please
 
  • #6
Hhhmmm...if you have a set of points, I can see being rotated with a transformation matrix...but a function? If you have a function f(x) and you "rotate" it 90 degrees...chances are it will stop being a function!...at least, in the sense of the new fnew(x) = trans(forig(x))
 
  • #7

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