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Trigonometry of a sphere

  1. Jun 11, 2009 #1
    Can someone just check my maths to see if this is correct.

    Hopefully, this should give the coordinates for a point on a sphere?

    x = radius x cos(vert angle) x sin(hoz angle)
    y = radius x cos(hoz angle)
    z = radius x sin(vert angle) x sin(hoz angle)
  2. jcsd
  3. Jun 11, 2009 #2


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  4. Jun 11, 2009 #3


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    In polar coordinates, [itex]x= \rho cos(\theta) sin(\theta)[/itex], [itex]y= \rho sin(\theta) sin(\phi)[/itex], [itex]z= \rho cos(\phi)[/itex]. There [itex]\theta[/itex] is what I think you are calling the "horizontal angle"- the angle between the positive x-axis and the line from (0,0,0) to the point (x,y,0)- also sometimes called the "longitude". [itex]\phi[/itex] is the "co-latitude", the angle between the z-axis and the line from (0,0,0) to (x,y,z). [itex]\rho[/itex] is the straight line distance between (0,0,0) and (x,y,z).

    For a sphere of radius R, this is [itex]x= R cos(\theta) sin(\theta)[/itex], [itex]y= R sin(\theta) sin(\phi)[/itex], [itex]z= R cos(\phi)[/itex].
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