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General solution

  1. Jun 17, 2009 #1
    1. The problem statement, all variables and given/known data
    determine the general solution of the equation:
    2sinx +cosecx -3 = 0


    2. Relevant equations



    3. The attempt at a solution
    Dont know what to do need help please.
     
  2. jcsd
  3. Jun 17, 2009 #2

    rock.freak667

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    What is cosecx equal to?

    When you find that, try multiplying by sinx throughout and see what happens from there.
     
  4. Jun 17, 2009 #3
    Okay I mapped sinx and got:
    2sin^{2}x-3sinx+sinx=0
    (2sinx-1)(sinx-1)=0
    2sinx=1 or sinx=1
    sinx=1/2

    Is this correct?
     
  5. Jun 17, 2009 #4

    Cyosis

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    You should learn to check your answers. Lets test it, if sinx=1/2 then the equation becomes:

    2*1/4-3*1/2+1/2=-1/2!=0

    So no it is not right.
     
    Last edited: Jun 17, 2009
  6. Jun 17, 2009 #5
    But x=30 or x=90
    then,
    substitute in the original equation of 2sinx + cosecx and you get the R.T.P answer of 3.
     
  7. Jun 17, 2009 #6

    Cyosis

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    I see what happened now. You meant to write 2sin^{2}x-3sinx+1=0 instead of 2sin^{2}x-3sinx+sinx=0. I checked your answer continuing from your first equation, which is wrong. All other steps are correct and your answers satisfy the original equation.
     
  8. Jun 17, 2009 #7
    Thanks for helping
     
  9. Jun 17, 2009 #8

    rock.freak667

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    Just remember that you were asked to give the general solution and not just solve in a given range.
     
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