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Math Help - using logarithm expression of sinh^-1

  1. #1
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    using logarithm expression of sinh^-1

    Hi all,
    I'm really stuck on a question and hoping someone can point me in the right direction.

    By using the logarithm expression of sinh-1(y), show that sinh-1(-y)=-sinh-1y

    So far im at
    sinh-1(-y)=ln((-y)+sqrt((-y)2+1))

    Thanks
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: using logarithm expression of sinh^-1

    So, you have:

    \sinh^{-1}(-y)=\ln(\sqrt{y^2+1}-y)

    My next step would be:

    \sinh^{-1}(-y)=-\ln\left(\frac{1}{\sqrt{y^2+1}-y} \right)

    Now, rationalize the denominator of the argument of the log function on the right.
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  3. #3
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    Re: using logarithm expression of sinh^-1

    Finished it, thanks. That was a big help
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  4. #4
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    Re: using logarithm expression of sinh^-1

    I'm really stuck on a question and hoping someone can point me in the right direction. cheap nfl hats hello kitty hats snapback for cheap
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