Explanation Given: ρ = csc ϕ cot ϕ Graph: In a spherical coordinate system , a point P in space is represented by an ordered triple ( ρ , θ , ϕ ) . ρ is the distance between P and the origin, ρ ≥ 0 . θ is the same angle used in cylindrical coordinates for r ≥ 0 . ϕ is the angle between the positive z − axis and the line segment O P → , 0 ≤ ϕ ≤ π . Note that the first and the third coordinates ρ and ϕ are non-negative. To convert from rectangular to spherical coordinates (or vice versa), use the conversion guidelines as shown below, To convert a point, Spherical to rectangular x = ρ sin ϕ cos θ y = ρ sin ϕ sin θ z = ρ cos ϕ Rectangular to spherical ρ 2 = x 2 + y 2 + z 2 tan θ = y x ϕ = arccos ( z x 2 + y 2 + z 2 ) To convert a set, use any of the above-mentioned equations as necessary. When plotting spherical coordinates, plot the radius first on the horizontal axis coordinates, then rotate the point about the angle θ about the origin and then rotate the point about the angle ϕ about the z- axis. The cartesian coordinate axes are often drawn in to make the graph more readable. While this method is easy to plot points, it often requires sophisticated software to plot a given function in 3D...

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

3rd Edition

ISBN: 9781319048518

Author: Colin Adams Jon Rogawski

Publisher: Macmillan Higher Education

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Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 12.7, Problem 64E

To determine

To sketch

The given set of points described in spherical coordinates

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Chapter 12.7, Problem 63E

Chapter 12.7, Problem 65E

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A factorization A = PDP 1 is not unique. For A= 7 2 -4 1 1 1 5 0 2 1 one factorization is P = D= and P-1 30 = Use this information with D₁ = to find a matrix P₁ such that - -1 -2 0 3 1 - - 1 05 A-P,D,P P1 (Type an integer or simplified fraction for each matrix element.)

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Chapter 12 Solutions

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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To sketch The given set of points described in spherical coordinates

To sketch The given set of points described in spherical coordinates

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Chapter 12 Solutions

To sketch

The given set of points described in spherical coordinates