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    • Thread Starter

    Say a question says "Using spherical polar co-ordinates (r, theta, phi) show that...". How do I know which of theta and phi is the angle from the vector to the positive z axis and which one is the plane polar angle? I'd expect that theta would be the plane polar angle to keep it similar to cylindrical polars and plane polars in 2D, but often it's the other way round. If the question doesn't say so, is there a way to tell which is which from the order of (r, theta, phi)?

    Conventionally, theta is the angle from the z axis and phi is the angle in the x-y plane (contrary to what Wikipedia said when I looked it up last). If the question doesn't say otherwise, that's how it is. In university they never said which was which in questions because it is assumed; the same way that in a plane polar question they wouldn't tell you that theta is the angle from the x-axis to r.
    • PS Helper

    PS Helper
    Some people use (r, \varphi) or (\rho, \varphi) for plane polars so the analogy's not quite so easy to carry. To be honest there are many different conventions for which thing refers to what; as long as you make it clear in one way or another what's what, it doesn't really matter. Normally it's clear by which you let have the range [0, 2\pi] and which you let have the range [0, \pi].

    I normally let \varphi be the azimuth ((x,y)-plane angle, range [0, 2\pi]) and \theta be the elevation (angle with the positive z-axis, range [0, \pi]).
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Updated: April 14, 2011

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