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Solution of equation

  1. Mar 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Find all solutions to the following equation: [tex]3tan(Inx)=2[/tex]



    3. The attempt at a solution

    [tex]tan(Inx)=2/3[/tex]

    [tex]Inx=arctan(2/3)[/tex]

    x=e^(arctan(2/3)
     
    Last edited: Mar 5, 2009
  2. jcsd
  3. Mar 5, 2009 #2

    lanedance

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    Hi Nyasha
    i think you mean ln(x) = arctan(2/3)?
     
  4. Mar 5, 2009 #3

    lanedance

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    note the potential for multiple solutions
     
  5. Mar 5, 2009 #4

    Yes thats what l meant and my answer is x=e^(arctan(2/3). How do you get multiple solutions ?
     
  6. Mar 5, 2009 #5

    lanedance

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    think about a graph of the function
    y = tanx
    it basically repeats along the axis every 2.pi

    when you take the arctan, you can think of it as picking a y value, tracing it out to across to where it intersects the curve, and dropping down to the x value, giving you
    x = arctan(y)

    how do you choose a curve to use....? multiple solutions... how many are there?
     
  7. Mar 5, 2009 #6
    Are you trying to say it has multiple solutions because the domain of arctan is from -∞ to ∞
     
  8. Mar 5, 2009 #7

    lanedance

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    no, to make it single valued, you must confine the range

    think of your diagram of y = tanx
    a vertical line will one graph
    A horizontal will intersect many

    try drawing y = arctanx
    what does it look like? will essentially be your prvious graph rotated by 90degreees
     
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