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Tan 50

  1. Aug 21, 2004 #1
    Hi
    can anyone tell me what is tan 50 in fractions?
    -benzun
     
  2. jcsd
  3. Aug 21, 2004 #2

    arildno

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    What's 50?
    Radians or degrees?
     
  4. Aug 21, 2004 #3

    arildno

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    I'll assume that "50" is in degrees:
    What you need is basically an expression for [tex]\cos(20)[/tex] , all the rest follow from this:

    1. [tex]\cos(60)=\cos(3*20)=4\cos^{3}20-3\cos(20)[/tex]
    by simple trigonometric identities.
    Hence, setting [tex]y=\cos(20)[/tex] you find the required value by solving for y in the equation:
    [tex]4y^{3}-3y=\frac{1}{2}[/tex] since [tex]\cos(60)=\frac{1}{2}[/tex]
    You need therefore the formula for roots of 3.degree polynomials.

    2. [tex]\cos(10)=\frac{1+y}{2}[/tex] by the half-angle formula.

    3. [tex]\cos(50)=\cos(60)\cos(10)+\sin(60)\sqrt{1-\cos^{2}(10)}[/tex]
    by the summation formula for cosine.

    4. By noting [tex]\sin(50)=\sqrt{1-\cos^{2}(50)}[/tex] you may find your expression for tan(50)
     
  5. Aug 24, 2004 #4
    sorry,
    i ment degrees only
    Thanks
    Is it possible to construct 50 degrees with a compas and scale only?
    -benzun
     
  6. Aug 24, 2004 #5
    Last edited by a moderator: Apr 21, 2017
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