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Unformatted text preview: containing the zaxis and the line O P , and the angle φ between the (positive) zaxis and the line O P (±igure 1.7 ). Of course, the spherical coordinate θ of P is identical to the cylindrical coordinate θ , and we use the same letter to indicate this identity. While θ is sometimes allowed to take on all real values, it is customary in spherical coordinates to restrict φ to 0 ≤ φ ≤ π . The relation between the cylindrical coordinates ( r,θ,z ) and the spherical coordinates ( ρ,θ,φ ) of a point P is illustrated in ±igure 1.8 (which is drawn in the vertical plane determined by θ ): 2 r = ρ sin φ θ = θ z = ρ cos φ. (1.7) 2 Be warned that in some of the engineering and physics literature the names of the two spherical angles are reversed, leading to potential confusion when converting between spherical and cylindrical coordinates....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Polar Coordinates

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