# Find locus of points in the plane [closed]

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

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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

$\sin(x+iy)*\sin(x-iy)=\sin^2(x)+\sinh^2(y)=1$