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Find the locus of points $(x,y)$ in the plane such that $\sin^2 x+\sinh^2 y=1$

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closed as not a real question by tomasz, Henning Makholm, Rudy the Reindeer, Quixotic, t.b. Sep 11 '12 at 16:14

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Which form do you need the solution in? You could just write $y=\pm \sinh^{-1}(\sqrt{1-\sin^2 x})$, or do you need something different from that? –  Henning Makholm Jan 22 '12 at 21:52
I would like it in a form that it is easy to draw and to understand. An hint is that, if we interpret $x$ and $y$ as the real and imaginary part of a complex number $z=x+iy$, I suspect it can be put in a neat form. –  quark1245 Jan 22 '12 at 21:56
Well, the shape of Savinov's plot, together with your hint, suggests that it could be something like $\cos(2(x+iy))=-1$, but I haven't checked the algebra on that. –  Henning Makholm Jan 22 '12 at 22:22

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