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Proof of sqrt(x^2)/x=sin (x)

  1. Oct 18, 2012 #1
    This isn't a homework question, but I felt it was appropriate....

    Proof that √(x^2)/x=sin(x)
     
  2. jcsd
  3. Oct 18, 2012 #2

    Mark44

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    You're going to have a very difficult time proving this - it isn't true.
     
  4. Oct 18, 2012 #3

    SammyS

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    I think that should be:

    [itex]\displaystyle \frac{\sqrt{x^2}}{x}=\text{sign}(x)\ .[/itex]
     
  5. Oct 18, 2012 #4

    Sorry that's what I thought i had...my bad :redface:
     
  6. Oct 18, 2012 #5
    Oh nevermind, so basically 1 = sinx .
    So x = arcsin 1
    What is really amasing is how they waste the ink to write X as sqrt(x²)
    Unless there's something hidden here, I cannot see the point.
    Well sin X = 1 if X is Pi and the way that the sine's sinusoidal graph repeats itself you can get the other possibilities for X.
     
    Last edited: Oct 18, 2012
  7. Oct 18, 2012 #6

    SammyS

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    Edit your original post, & make a note there that you've edited it.
     
  8. Oct 18, 2012 #7

    Mark44

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    No for a couple of reasons. First, the OP meant sign(x) not sin(x). Second,
    ## \frac{\sqrt{x^2}}{x} \neq 1##
    No. x ≠ ##\sqrt{x^2}##
     
  9. Oct 18, 2012 #8
    Wait, x =/= sqrt(x²)??

    I cannot see what you are trying to say - do you mean that sqrt(x²) = +/- X?
    This is actually something I was arguing over with my math's lector and he said that the square root of X or X² for that matter, is defined as sqrt(X²) = |X|

    And after thinking about it, i thought about

    A^x = B
    x lnA = lnB
    if B were negative then this wouldn't hold true and the only explanation is that Sqrt(A²) = |A|
     
  10. Oct 18, 2012 #9

    Mark44

    Staff: Mentor

    Yes, that's exactly what I mean. As an example, do you think that ##\sqrt{(-2)^2} = -2##?
    No, I don't mean that either. The square root of a nonnegative expression produces a single value, not two of them, as ± x implies.
    Your lecturer is correct.
    Also, your second step isn't valid if A ≤ 0, because ln(A) wouldn't be defined.
     
  11. Oct 20, 2012 #10
    the reason why x is not equal to root of x squared is this-

    If a, b are positive numbers, and you take root of that (in complex numbers, of course), then the relation √-a × √-b = √(-×-)ab = √(+ab) does not hold valid

    instead, √-a × √-b = i√a × i√b = -√ab

    that's the reason.... and also, √x2 / x should be equal to signum function of x which equals modulus of x divided by x
     
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