Transcription of Cylindrical and Spherical Coordinates
1 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 .
2 (1, /2, 1)7EX 4 Make the required change in the given ) x2 - y2 = 25 to Cylindrical ) x2 + y2 - z2 = 1 to Spherical ) = 2cos to Cylindrical 4 Make the required change in the given equation (continued).d) x + y + z = 1 to Spherical ) r = 2sin to Cartesian ) sin = 1 to Cartesian coordiantes.
