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Cylindrical and Spherical Coordinates

1 Cylindrical and Spherical Coordinates 2We can describe a point, P, in three different Coordinatesx = r cos r = x2 + y2y = r sin tan = y/xz = zz = zSpherical Coordinatesx = sin cos = x2 + y2 + z2y = sin sin tan = y/xz = cos cos = x2 + y2 + z2z3 Easy Surfaces in Cylindrical Coordinatesa) r =1b) = /3c) z = 4 Easy Surfaces in Spherical Coordinatesa) =1b) = /3c) = /44EX 1 Convert the Coordinates as indicateda) (3, /3, -4) from Cylindrical to ) (-2, 2, 3) from Cartesian to 2 Convert the Coordinates as indicateda) (8, /4, /6) from Spherical to ) (2 3, 6, -4) from Cartesian to 3 Convert from Cylindrical to Spherical Coordinates .

5 EX 2 Convert the coordinates as indicated a) (8, π/4, π/6) from spherical to Cartesian. b) (2√3, 6, -4) from Cartesian to spherical.

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