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Show sin(1), in degrees, is algebraic over the rationals

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data

    show sin(1), in degrees, is algebraic over the rationals

    3. The attempt at a solution

    I want to find the minimal polynomial that has root sin(pi/180). Ya that's all I got.
     
  2. jcsd
  3. Apr 21, 2009 #2
    Well, here's one way.

    sin(pi/5) = (1/4)*\sqrt{ 10 - 2*\sqrt{5} }


    Here's another.

    sin z = ( e^{iz} - e^{-iz} )/(2i)
     
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