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Atan2 formula

  1. Jun 5, 2010 #1
    Hello, it is mentioned http://en.wikipedia.org/wiki/Atan2#Definition" that using the tangent half-angle formulas it is possible to express the function atan2 as:

    [tex]\mathrm{atan2}(y,x)=2\mathrm{arctan}\frac{y}{\sqrt{x^2+y^2}+x}[/tex]

    How can I derive this result?
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Jun 5, 2010 #2

    tiny-tim

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    Put y = rsinθ, x = rcosθ, then y/(√(x2 + y2) + x) = sinθ/(1 + cosθ),

    which you should be able to prove is tan(θ/2) :wink:
     
  4. Jun 6, 2010 #3
    Thanks!
    Now it´s clear where that formula came from.
     
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