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Thread: Hyperbolic Identities - need help

  1. #1
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    Hyperbolic Identities - need help

    Im kinda working ahead of myself on my assignment and I am stuck on this question:

    Solve the following for X

    cosh^2(x) + 5sinh(x) + 6 = 1 + sinh^2 (x)

    Any help would be great!

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  2. #2
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    Re: Hyperbolic Identities - need help

    Quote Originally Posted by FooFightin View Post
    Im kinda working ahead of myself on my assignment and I am stuck on this question:

    Solve the following for X

    cosh^2(x) + 5sinh(x) + 6 = 1 + sinh^2 (x)
    Because $\cosh^2(x)=1+\sinh^2(x)$ you really have just
    $5\sinh(x)+6=0\\\sinh(x)=\dfrac{-6}{5}$

    What can you do now?
    Thanks from FooFightin
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  3. #3
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    Re: Hyperbolic Identities - need help

    Thanks Plato that was a massive help! I knew nothing about hyperbola so I went on to read a bit more after looking at your reply and came up with this which I hope is correct!

    (cosh^2(x)-sinh^2(x)0+5sinh(x)=1-6

    Using identity (cosh^2(x)-sinh^2(x))=1

    1+5 sinh(x) = -5
    5sinh(x) = -5-1
    5 sinh(x) = -6
    sinh(x)=-6/5
    sinh(x)=-1.2
    sinh^-1(-1.2)=x

    x = -1.015973134
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