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Homework Help: Simple (or should be) Trigonomic question

  1. Oct 23, 2009 #1


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    1. The problem statement, all variables and given/known data

    I'm making a program that tracks an object moving along the surface of a sphere (earth). I'm using a set of Cartesian coordinates who origin is the center of the earth and Z directed through the north pole, X the greenwich meridian at the equator, and Y is 90 degrees to everyone else.

    Given a Lat/Long value I can convert into a position vector by doing:

    phi = (90 - lat)*pi/180
    theta = long*pi/180

    vector.x = sin(phi)*cos(theta)
    vector.y = sin(phi)*sin(theta)
    vector.z = cos(phi)

    After moving my object around I need to convert it back into lat / long. At the moment I'm just trying to take a position in Lat/long, convert it into my position vector, draw it on a sphere , then convert it back.

    I know my conversion TO the position vector is working properly since it points to the right spot on a sphere. What I can't get right is the conversion FROM the vector back to lat long.

    2. Relevant equations
    See above.

    3. The attempt at a solution

    I thought I could find phi from the Z component, then solve X and Y simultaneously for theta. So since Z = cos(phi), I thought easy phi = 1/cos(Z).

    Only that didn't work. Sat down, thought for a bit, played around with cos and sec, and realized cos and sec aren't inverse operations (which I thought for sure they were) so sec(cos(a)) != a.

    There's a simple little rule for finding going from A = cos(angle), to an expression for the angle, when you know A. Can someone please tell me what it is ? I've spent hours on something I thought I learnt back in Highschool !
  2. jcsd
  3. Oct 23, 2009 #2


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    Staff: Mentor

    Is there a reason you aren't using spherical coordinates instead of cartesian coordinates? Seems like you're making it extra hard on yourself.

    Here are some trig notes from wikipedia if they help:


  4. Oct 23, 2009 #3


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    We were told to use Cartesian, not spherical. Gonna have another read through the wiki page, its gotta be there somewhere.
  5. Oct 23, 2009 #4


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    I worked it out. Turns out sec is the reciprocal of cos, arccos is the inverse function. I'm annoyed I forgot something so basic, but at least its all working now.
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