Spherical Coordinates Conversion Chart

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Spherical Coordinates Conversion Chart

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Spherical Coordinates Conversion Chart

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So given a point in spherical coordinates the cylindrical coordinates of the point will be r sin z cos r sin z cos Note as well from the Pythagorean theorem we also get 2 r2 z2 2 r 2 z 2 Next let s find the Cartesian coordinates of the same point To do this we ll start with the Examples on Spherical Coordinates Example 1 Express the spherical coordinates 8 3 6 in rectangular coordinates Solution To perform the conversion from spherical coordinates to rectangular coordinates the equations used are as follows x sin cos 8 sin 6 cos 3 x 2 y sin sin The backward conversion has similar domain restrictions for the spherical coordinates The restrictions have the radius r ranging from to infinity the polar angle ranging from 0 to 90 or radians and the azimuth angle ranging from 0 to 360 or 2 radians Example Convert the Cartesian coordinates 1 2 3 on the third dimensional plane