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I know that it is possible to rotate conic sections a certain number of degrees. How do you rotate other equations in general, such as $y = \sin^2 \theta$ or $x = y^3$? Thanks!

Edit: One thing I forgot to ask previously was how do you tell if an equation, when rotated a certain number of degrees, will be a function after rotation?

PreciselyT
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    Is it possible In what sense "possible"? It is of course possible to rotate anything by any angle (degrees or not), so the question doesn't make much sense at face value as written now. – dxiv Mar 11 '18 at 06:32
  • Ok. I edited it to make it more specific – PreciselyT Mar 11 '18 at 06:46
  • How do you rotate the "conic sections", and where does the same fail when applied to non-conics? – dxiv Mar 11 '18 at 06:50
  • Do you want to rotate the curves within the plane about some point in the plane, or do you want to rotate them about a line in the plane so that the curve traces out a surface in $\mathbb{R}^3$? – John Wayland Bales Mar 11 '18 at 07:00
  • @John Wayland Bales I wanted to rotate curves within a plane about some point. – PreciselyT Mar 11 '18 at 07:08
  • Your first "equation" is an expression, not an equation. Do you mean the equation $y=\sin^2\theta$? And by "rotating an equation" do you mean deriving a new equation whose graph is the rotation of the graph of the original equation? (I don't mean to be pedantic, but precision is important in questions like these.) – Rory Daulton Mar 11 '18 at 12:03
  • @RoryDaulton Yes that is what I mean. Thanks. – PreciselyT Mar 12 '18 at 03:44
  • This explains how to rotate about the origin: https://math.stackexchange.com/questions/17246/is-there-a-way-to-rotate-the-graph-of-a-function – John Wayland Bales Mar 12 '18 at 06:18
  • @JohnWaylandBales Thank you – PreciselyT Mar 18 '18 at 00:31

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