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Finding sine and cosine formulas

  1. Oct 31, 2007 #1
    [SOLVED] Finding sine and cosine formulas

    1. The problem statement, all variables and given/known data
    If sinx/siny = 1/2 and cosx/cosy = 3 prove:

    sin (x + y) = 7/3 sinx cosx


    2. Relevant equations
    sin (x + y) = sinx cosy = cosx siny


    3. The attempt at a solution

    Can someone please give me a hint so that I can start? Thanks.
     
  2. jcsd
  3. Oct 31, 2007 #2

    rock.freak667

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    Well fine cosy in terms of cosx from the 2nd formula and find siny in terms of sinx from the 1st formula and sub into the LHS of the proof
     
  4. Oct 31, 2007 #3
    Ok, here it goes:

    * sinx/siny = 1/2

    siny = 2sinx

    * cosx/cosy = 3

    cosy = cosx/3


    sin(x + y) = sinx cosy + cosx siny
    = cosx/3 + 3 X 2sinx
    = cosx/3 + 6sinx
    = 7/3 sinx cosx


    Is this possibly right?
    Please help. Thanks
     
  5. Oct 31, 2007 #4

    rock.freak667

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    well that is correct...but you should put in the sinx and cosx in the 2nd and 3rd lines...or else it may seem weird that you simply got back the sinx and cosx at the end
     
  6. Oct 31, 2007 #5
    Well, If I put back sinx and cosx, then how will I get rid of them in the end?
     
  7. Oct 31, 2007 #6

    rock.freak667

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    sin(x + y) = sinx cosy + cosx siny
    = (sinxcosx)/3 + 2sinxcosx
    =[itex]\frac{7sinxcosx}{3}[/itex]
     
  8. Nov 1, 2007 #7
    Thanks very much rock.freak667. I finally get this.
     
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