OK, so I'm currently failing to figure this out...

How do you compute the smallest possible (axis-aligned) bounding box for 
an ellipse (which is not necessarily axis-aligned)?

Apparently such an ellipse can be represented as

   X(t) = Xc + A cos t cos K - B sin t sin K
   Y(t) = Yc + A cos t sin K + B sin t cos K

Clearly you need to find the minimum and maximum values for X(t) and 
Y(t). But I am apparently too stupid to do this. (And even Wolfram Alpha 
can't work it out. Oh, it'll give me the answer if I remove all the 
symbolic constants with actual numbers, but that's no help at all...)

It strikes me that the sum of two sine waves of identical frequency is 
another sine wave, but I can't seem to apply this fact to obtain a result.

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