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11.7

11.7. Cylindrical and Spherical Coordinates. The Cylindrical Coordinate System. In a cylindrical coordinate system, a point P in space is represented by an ordered triple is a polar representation of the projection P in the xy-plane. z is the directed distance from to P.

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11.7

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  1. 11.7 Cylindrical and Spherical Coordinates

  2. The Cylindrical Coordinate System • In a cylindrical coordinate system, a point P in space is represented by an ordered triple • is a polar representation of the projection P in the xy-plane. • z is the directed distance from to P.

  3. Figure 11.66

  4. Conversions: Cylindrical to rectangular Rectangular to cynlidrical

  5. Examples: • Convert from cylindrical to rectangular coordinates • Find an equation in cylindrical coordinates for the rectangular equation • Find an equation in rectangular coordinates for the equation in cylindrical coordinates and sketch its graph.

  6. Spherical Coordinates • In a spherical coordinate system, a point P in space is represented by an ordered triple 1. is the distance between P and the origin, 0 2. is the same angle used in cylindrical coordinates for r greater than or equal to 0. 3. is the angle between the positive z-axis and the line segment from the origin to the point P

  7. Figure 11.75

  8. Conversions • Spherical to Rectangular • Rectangular to spherical:

  9. More Conversions • Spherical to cylindrical (r 0) • Cylindrical to Spherical (r 0)

  10. More Examples: 1) Convert the point from spherical to rectangular • Find an equation in rectangular coordinates and graph. 3) Convert the equation to cylindrical and spherical,

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