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Convert this rectangular coordinate system point to spherical coordinate system

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data

    The point is (0, -8, 0)
    r≥0
    0≤θ≤2∏
    0≤[itex]\varphi[/itex]≤∏

    2. Relevant equations



    3. The attempt at a solution

    So here is what I've done so far:

    I know that r=8 because x and z are 0

    I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation (which is the only one I know for this)

    cos(θ)=y/x

    Also, I am confused about [itex]\varphi[/itex]. I know that:

    tan([itex]\varphi[/itex])=y/x, but y is negative, and x is zero. I know the value of arctan(∞) as well as arctan(-∞) but which one do I use? I am so confused. Thanks!
     
  2. jcsd
  3. Mar 30, 2012 #2
    Draw a diagram and plot your point, then go from there by comparing to this.
     
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