#Rotating a #Point about the origin, through some #Angle θ is something that is taught in school #maths class, usually in #CartesianCoordinates, by multiplying the #Coordinates by a the rotation #Transformation #Matrix. What’s not generally taught is that you can apply the same transformation to any #Function y=f(x). All you need to do is replace
x by xcosθ + ysinθ
and y by -xsinθ+ysinθ.
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Of course, this leads to an implicit rather than an explicit expression involving the variables. and not all #software is capable of plotting such functions. Happily, #WxMaxima has that ability.
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And so, here are four functions to demonstrate it. The default resolution of the plotting routine is crude, leading to #Aliasing and so the mesh has to be refined somewhat.
Here are three #ConicSections and one #Trigonometric functions.
An #Ellipse
A #Parabola.
A #Hyperbola.
A rotating #Tangent function.
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Khurram Wadee ✅