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Math Help - hyperbolic functions

  1. #1
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    hyperbolic functions

    Prove that the  sinh^{-1}x = ln(x+\sqrt{x^{2}+1})

    is  sinh^{-1}x = \frac{1}{sinhx} ?

    if so than could I write

     sinh^{-1}x  = \frac{2}{e^{x}-e^{-x}}

    and am not sure how to got from there, any help appreciated.
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  2. #2
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    Re: hyperbolic functions

    Quote Originally Posted by Tweety View Post
    Prove that the  sinh^{-1}x = ln(x+\sqrt{x^{2}+1})
    is  sinh^{-1}x = \frac{1}{sinhx} ?
    First of all  \sinh^{-1}x \not = \frac{1}{\sinh x}

    Many of us hate that notation.
     \sinh^{-1}x means the inverse of the hyperbolic-sine function

    Find the inverse of y=\frac{e^x-e^{-x}}{2}.
    Last edited by Plato; October 25th 2012 at 08:26 AM.
    Thanks from Siron and Tweety
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  3. #3
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    Re: hyperbolic functions

    so  sinh^{-1}x = \frac{2}{e^{x}-e^{-x}} ?
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  4. #4
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    Re: hyperbolic functions

    Quote Originally Posted by Tweety View Post
    so  sinh^{-1}x = \frac{2}{e^{x}-e^{-x}} ?
    Absolutely not true.

    Do you even know what an inverse is?

    Do you even know how to find the inverse of a given function?
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  5. #5
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    Re: hyperbolic functions

    I do^^ but I am just a bit confused as to how to do this question.
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  6. #6
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    Re: hyperbolic functions

    Quote Originally Posted by Tweety View Post
    I do^^ but I am just a bit confused as to how to do this question.
    Solve x=\frac{e^y-e^{-y}}{2} for y.
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  7. #7
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    Re: hyperbolic functions

    This might be difficult to see how to solve. You can probably see e^x=\cosh{x}+\sinh{x}, but it might not be as easy to see \cosh^2{x}-\sinh^2{x}=1.

    - Hollywood
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