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Okay, I got it. Your equation was correct, but I initally thought that it needed something to bound the rectangle from having an infinite area with no boundaries. You didn't show the implied step of substituting the cos and sin in for x and y, which I didn't notice. That substitution is what bounds it, and that's what I missed. I knew that your equation was that of the rectangle the whole time, I just missed where you bounded the equation.
Sorry for the confusion.
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