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.
Arc length of level sets
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analysis
multivariable-calculus
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0Are 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... – 2011-03-29
1 Answers
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The length is either 0 or infinity, depending on A and B, because the function z is periodic in x and in y.
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0@Pacciu: Thanks, I didn't realize I could edit the post, this is my first time on stackexchange. I think the problem should be more easily understood now. – 2011-03-29