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Finding sin(7.5)

  1. Nov 8, 2007 #1
    [SOLVED] Finding sin(7.5)

    1. The problem statement, all variables and given/known data
    Find sin(7.5) using [tex]sin\frac{x}{2} = \sqrt{(\frac{1 - cosx}{2})}[/tex]


    2. Relevant equations
    sin2x = 2sinxcosx
    cos(x-y) = coxcosy + sinxsiny


    3. The attempt at a solution

    [tex]sin\frac{15}{2} = \sqrt{(\frac{1 - cos15}{2})}[/tex]

    = [tex]\sqrt{(\frac{1 - cos(45-30)}{2})}[/tex]

    = [tex]\sqrt{(\frac{1 - (\frac{\sqrt(2)+\sqrt(6)}{4})}{2})}[/tex]


    After this I don't know what to do. I would like some help please. Thanks.
     
  2. jcsd
  3. Nov 8, 2007 #2

    Avodyne

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    Science Advisor

    I think you're done (assuming 7.5 means 7.5 degrees, not 7.5 radians). Unless you want to plug it into a calculator and get a number.
     
  4. Nov 8, 2007 #3
    In our answer sheet, the answer for this question is:

    [tex]\frac{5 + \sqrt{5}}{8}}[/tex]

    or

    [tex]\frac{5 - \sqrt{5}}{8}}[/tex]

    So I am really confused as to how to get 8 as the denominator. Please help. Thanks.

    (Note: 7.5 is degrees.)
     
    Last edited: Nov 8, 2007
  5. Nov 8, 2007 #4

    Dick

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    Homework Helper

    You don't want to get those answers. They are wrong. And how can there be two of them? You are right.
     
  6. Nov 8, 2007 #5
    Yea, I think there must be a typo on the answer sheet. Anyways, thanks to both Dick and Avodyne for analyzing the problem.
     
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