100 likes | 254 Views
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.
E N D
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.
Conversions: Cylindrical to rectangular Rectangular to cynlidrical
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.
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
Conversions • Spherical to Rectangular • Rectangular to spherical:
More Conversions • Spherical to cylindrical (r 0) • Cylindrical to Spherical (r 0)
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,