# Spherical Coordinates

## Main Question or Discussion Point

Just curious, why is $$\phi$$ 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, $$\theta$$ is calculated from the +x axis to the +y axis (counterclockwise) for position vectors.

*So, why not extrapolate alphabetically, to have the $$\phi$$ be the angle between the +y axis and the position vector of a point as projected onto the yz plane?

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## Answers and Replies

arildno
Homework Helper
Gold Member
Dearly Missed
Use whatever convention you like, there is no general agreement on this issue.

arildno said:
Use whatever convention you like, there is no general agreement on this issue.
But nowhere have I found $$\phi$$ calculated as the angle between the +y axis and the position vector of a point, projected onto the yz plane...

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).