# Arc length of level sets

I have a function $z = B \sin x \ \sin y+\cos x \ \cos y$. Where $0 \leq x \leq \pi$ and $0 \leq y \leq \pi$. I need to find the length of the curve that describes a level set for any value of $B$. That is, if I set $z = A$ (where $A$ is some scalar constant), what is the length of the level curve for any value of the parameter $B$. Obviously some symmetry can be exploited to solve the problem, but I'm having trouble figuring out how to derive the length.

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Are you sure the variables $x,y$ have not to satisfy some bound (e.g., $-\pi\leq x,y\leq \pi$)? For otherwise the problem is meaningless... – Pacciu Mar 29 '11 at 16:55

@okj: Then, why don't you edit your post and write "with $0\leq x,y\leq \pi$" somewhere in it? ;-) – Pacciu Mar 29 '11 at 22:26