(a) The following points are given in cylindrical coordinates; express each in rectangular coordinates and spherical coordinates Cylindrical (r, 0, z) Rectangular Spherical (x, y, z) (P, 0, 9) (1, 45°, 3)| (| 1 1 3 V2, 45°, tan 1 3 (플→) (C (0, 45°, 9)

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter12: Conic Sections
Section12.5: Rotation Of Axes
Problem 1E: Suppose the x- and y-axes are routed through an acute angle to produce the new X- and Y-axes. A...
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(a) The following points are given in cylindrical coordinates; express each in rectangular coordinates and spherical coordinates.
Cylindrical
(r, 0, z)
Rectangular
(x, y, z)
Spherical
(p, 6, ф)
(1, 45°, 3)|(
1
1
3
V2, 45°, tan
(0, 45°, 9)
(1. 0)
(6, -)
(b) Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
Rectangular
(х, у, 2)
Spherical
(p, 0, p)
Cylindrical
(r, 0, z)
(4, 2, -4)
(0, 3, 4),
(V2, 1, 1)
(-2/3, -2, 3) | (
Transcribed Image Text:(a) The following points are given in cylindrical coordinates; express each in rectangular coordinates and spherical coordinates. Cylindrical (r, 0, z) Rectangular (x, y, z) Spherical (p, 6, ф) (1, 45°, 3)|( 1 1 3 V2, 45°, tan (0, 45°, 9) (1. 0) (6, -) (b) Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates. Rectangular (х, у, 2) Spherical (p, 0, p) Cylindrical (r, 0, z) (4, 2, -4) (0, 3, 4), (V2, 1, 1) (-2/3, -2, 3) | (
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