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Unformatted text preview: Math 200, Spring 2010 Handout 5 Section 12-7 Cylindrical and Spherical Coordinates Section 13-1 Vector-Valued Functions Cylindrical Coordinate System In the cylindrical coordinate system , a point P in three dimensional space is represented by the ordered triple ( ) , , r z θ , where r and θ are polar coordinates of the projection of P onto the xy-plane and z is the directed distance from the xy-plane to P . To convert from cylindrical to rectangular coordinates, use: cos sin x r y r z z θ θ = = = To convert from rectangular to cylindrical coordinates, use: 2 2 2 tan y r x y x z z θ = + = = 1. Plot the point whose cylindrical coordinate are ( ) 2,3 4, e π − and find the rectangular coordinates of this point. 2. Change ( ) 2 3, 2, 1 − − from rectangular to cylindrical coordinates. Level Surfaces in Cylindrical Coordinates The level surfaces of a coordinate system are the surfaces obtained by setting one of the coordinates equal to a constant. In rectangular coordinates , the level surfaces are the planes x x = , y y = , and z z = , where , , x y and z are constants. In cylindrical coordinates , there are three types of level surfaces: (1) The surface r R = is the cylinder of radius R consisting of all points at distance R from the z-axis. (2) The surface θ θ = consists of all points in the half-plane that project onto the ray θ θ = ( the standard convention in cylindrical coordinates is that r ≥ )....
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This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.
- Spring '10