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Math Help - converting rectangular to spherical coordinates

  1. #1
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    converting rectangular to spherical coordinates

    Question:
    Convert the point from rectangular coordinates to spherical coordinates.


    a.
    b.
    c.
    d.
    e.
    Relevant equations :
    tanθ = y/x
    ρ = √(x≤+y≤+z≤)
    Φ = arccos(z/ρ)

    Solution attempt:
    ρ=√(7≤+(7√3)≤+14≤) = 14√2
    tanθ = 7√3/-7 = -√3 arctan(-√3) = -Π/3
    Φ = arccos(14/14√2) = Π/4



    Now my issue is that as you can see -Π/3 is not an option in the multiple choice for θ. I assume the answer is then Π/3 but Iím a little unsure why I didnít get that as my answer.
    Last edited by shmiks; September 21st 2013 at 10:30 PM.
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  2. #2
    MHF Contributor
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    Re: converting rectangular to spherical coordinates

    Hey shmiks.

    Hint: 7√3/7 = 1/√3. You wrote x as 7 in calculating rho: is it 7 or -7?
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