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MissMousey Problem: For each of the following transformations (u,v) = f(x, y): (i) compute the Jacobian det Df, (ii) draw a sketch of the images of some of the lines x = constant and y = constant in the uv-plane, and (iii) find the formulas for the local inverses of f when they exist.
(a) u = (e^x)(cosy), v = (e^x)(siny)
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I've completed (i) and (ii) but I'm stuck on (iii). I know I have to solve for x and y but don't know how to start. Hints?