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You are able to rotate any function by an arbitrary angle around the origin using the formula, $$y\cos\theta-x\sin\theta=f(x\cos\theta+y\sin\theta)$$You can also do similar rotations for polar graphs, or multivariable functions; however, what would the actual purpose of doing so be? Possibly making a certain problem easier to evaluate or does it have some application in real life?

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It's used in almost every field of physics and engineering. You write a matrix associated with the rotation and you apply it to your vector.

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  • $\begingroup$ What would be a specific example of this? I tried searching myself but I couldn't find anything regarding my question. $\endgroup$ – Anthony P Feb 20 at 1:53
  • $\begingroup$ For example, I work in a computational fluid dynamics software. I need to make the plane's wing have different angle (angle of attack) to find the best angle (stall angle). Unfortunately you can't move the wing in that software, so what I do is that I rotate the wind and my wing stays horizontal. Then I applied a rotation of parameter the angle theta to my vector of wind. Then I start like 1000 computations for angles between 0° and 30° and then I get a nice graph. $\endgroup$ – PackSciences Feb 20 at 7:45

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