Convert the following point from rectangular to spherical coordinates:
(1, −√3, 2√3).

I found the answer to be (4, -pi/3, 0.5235987755983), but my online homework is stating that my middle coordinate (-pi/3) is incorrect. I put this into an online calculator and it's giving me the same answer. Am I missing something?

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asked by EKM
  1. going from (x,y,z) to (r,Ø,θ),
    r^2 = x^2+y^2+z^2 = 1+3+12 = 16, so r=4
    tanØ = y/x = -√3, so Ø = -π/3 or 2π/3
    cosθ = z/r = √3/2, so θ = ±π/6

    (1, −√3) is in QIV, so Ø = -π/3
    z > 0, so θ = π/6
    (r,Ø,θ) = (4,-π/3,π/6)

    Looks good to me.

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    posted by Steve

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