Explanation Given: ( 3 2 , 3 2 , 1 ) Key Concept Applied: In rectangle coordinate system a point P in space is represented by the ordered triple ( x , y , z ) . Here the point P can also be taken as the (signed) distances from P to the three planes defined by the three axes. If the axes are named x , y , a n d z , then the x − coordinate is the distance from the plane defined by the y − a n d z − axes. The distance is to be taken with the + o r − sign, depending on which of the two half-spaces separated by that plane contains P. The y − a n d z − coordinates can be obtained in the same way from the x z − a n d x y − planes respectively. To convert from rectangular to spherical coordinates we use the relations ρ = x 2 + y 2 + z 2 , θ = tan − 1 ( y x ) , ϕ = cos − 1 ( z ρ ) Formula Used: Convert from rectangular to spherical coordinates ρ = x 2 + y 2 + z 2 θ = tan − 1 ( y x ) ϕ = cos − 1 ( z ρ ) Calculation: Convert ( 3 2 , 3 2 , 1 ) from rectangular to spherical coordinates Step 1: In rectangular coordinate system a point P in space is represented by the ordered triple ( x , y ,

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Author: FRANZOSA

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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 13.7, Problem 40E

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To convert:

From rectangular to spherical coordinates

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Chapter 13.7, Problem 39E

Chapter 13.7, Problem 41E

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Chapter 13 Solutions

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Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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From rectangular to spherical coordinates

Solution Summary: The author explains how to convert from rectangular to spherical coordinates.

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To convert: From rectangular to spherical coordinates

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Chapter 13 Solutions

To convert:

From rectangular to spherical coordinates