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Trig substitution

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data
    If sin54=P, express the following in terms of p, with out using a calculator.
    1] cos18
    2] [tex]\frac{tan27+cot63}{1+tan207.cot117}[/tex]


    2. Relevant equations



    3. The attempt at a solution

    1] cos18=sin(90-18)
    =sin(72)

    sin72=sin(180-108)
    =sin(180-108)
    =sin180.cos108-cos180.sin108
    =0-(-sin108)
    =sin108

    sin108=2.sin54.cos54
    =2pcos54.[tex]\sqrt{1-p^{2}}[/tex]



    2] =[tex]\frac{2tan27}{1-tan27.tan27}[/tex]

    =[tex]\frac{2tan27}{1-tan^{2}27}[/tex]

    =tan2(27)

    =tan54

    =[tex]\frac{p}{\sqrt{1-p^{2}}}[/tex]
     
  2. jcsd
  3. Jun 16, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor


    "P" or "p"? You shouldn't use both to mean the same thing.

    Well, you mean, of course,
    [tex]sin(108)= 2p\sqrt{1- p^2}[/tex]
    Also you haven't finished the problem. Yes, cos(18) is equal to that but you should write that explicitely:
    [tex]cos(18)= 2p\sqrt{1- p^2}[/tex]
    I see nothing wrong with (2).
     
  4. Jun 16, 2009 #3
    Thanks, I made a few typing errors.
     
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