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Unformatted text preview: x = cos 2 z y = sin 2 z such a description gives us far less insight into the curve than the parametrized version. As another example, let us parametrize the locus of the pair of equations x 2 + y 2 = 1 y + z = 0 which, geometrically, is the intersection of the vertical cylinder x 2 + y 2 = 1 with the plane y + z = 0 . The projection of the cylinder on the xy-plane is easily parametrized by x = cos t y = sin t...
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- Fall '08