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Coordinate Systems in 3D Space: Cylindrical and Spherical Conversion Methods

Learn about cylindrical and spherical coordinate systems, convert between Cartesian and cylindrical coordinates, and understand the transformation between Cartesian and spherical coordinates. Explore the representation of points in space and their conversion methods.

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Coordinate Systems in 3D Space: Cylindrical and Spherical Conversion Methods

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  1. Section 13.7 Cylindrical and Spherical Coordinates

  2. THE CYLINDRICAL COORDINATE SYSTESM In the cylindrical coordinate system, a point P in space is represented by the ordered triple (r,θ, z), where 1. r andθ are polar coordinates of the projection of P onto the xy-plane; 2. z is the directed distance from the xy-plane to P.

  3. CONVERTING BETWEEN CARTESIAN AND CYLINDRICAL COORDINATES Cylindrical to Cartesian Cartesian to Cylindrical

  4. THE SPHERICALCOORDINATE SYSTEM In the spherical coordinate system, the point P is represented by (ρ, θ,φ) where • ρ is the distance between P and the origin O, ρ ≥ 0; • θ is the same angle used in cylindrical coordinates for r ≥ 0; and • φ is the angle between the positive z-axis and the line segment OP. 0 ≤ φ ≤ π.

  5. CONVERTING BETWEEN CARTESIAN AND SPHERICAL COORDINATES Spherical to Cartesian Cartesian to Spherical

  6. CONVERTING BETWEEN CYLINDRICAL AND SPHERICAL COORDINATES Cylindrical to Spherical Spherical toCylindrical

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