Unformatted text preview: ρ = 2, ≤ θ ≤ π 2 , and 0 ≤ φ ≤ π 4 . (5) Use spherical coordinates to describe the region above the xyplane between the spheres of radius 1 and 3 centered at the origin. (This is the reverse of problem 4.) (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Determine the Cartesian equation of the surface with spherical coordinate equation ρ = 2 cos θ sin φ2 sin θ sin φ + 2 cos φ . It turns out this describes a sphere. What is the center and radius of this sphere? 1...
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 Winter '11
 JerryMetzger
 Calculus, Multivariable Calculus, Polar coordinate system, Coordinate systems, spherical coordinate

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