Spherical Coordinates

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  • #1
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Just curious, why is [tex] \phi [/tex] calculated as the angle between the +z axis and a position vector of a point of a function, as projected onto the yz plane? Why this convention?

In polar & cylindrical, [tex] \theta [/tex] is calculated from the +x axis to the +y axis (counterclockwise) for position vectors.

*So, why not extrapolate alphabetically, to have the [tex] \phi [/tex] be the angle between the +y axis and the position vector of a point as projected onto the yz plane? :smile:
 
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  • #2
arildno
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Use whatever convention you like, there is no general agreement on this issue.
 
  • #3
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arildno said:
Use whatever convention you like, there is no general agreement on this issue.
But nowhere have I found [tex] \phi [/tex] calculated as the angle between the +y axis and the position vector of a point, projected onto the yz plane...
 
  • #4
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You will see why once you start working with problems involving these. For example, take the intersection between a sphere and a cone (I posted about this before). This can be computed by a double integral, but if you use a triple integral and spherical coordinates, it becomes much simpler (thanks to HallsofIvy on this).
 

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