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Math Help - Hyperbolic functions and their values :(

  1. #1
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    Unhappy Hyperbolic functions and their values :(

    Some help in the right direction? I have no idea where to start:

    Question:
    If sinh x = 3/4, find the values of the other hyperbolic functions at x.


    I would greatly appreciate any help! I'm taking a distance course and learning all this by yourself is tough!!

    cheers,

    klooless
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  2. #2
    Member Ruun's Avatar
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    Hint:

    cosh^2(x) - sinh^2(x) =1
    Last edited by Ruun; June 10th 2009 at 12:51 AM.
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by Ruun View Post
    sinh^2(x) - cosh^2(x)=1


    I think you meant \cosh^2(x) - \sinh^2(x)=1.
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  4. #4
    Member Ruun's Avatar
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    Yes! you're right, thanks for the correction
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  5. #5
    Super Member craig's Avatar
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    When remembering the differences between the normal trigonometrical functions and their hyperbolic alternatives, I find it useful to use the,

    2 sinhs change the sign.
    That is, if there are two sinhs multiplied together, as in the sin^2, the you change the sign that you would use normally, in this case it is a minus instead of a plus.
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  6. #6
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    Still having trouble; hyperbolic functions...

    Thank you to Ruun, flyingsquirrel and Craig for giving me tips to solve;

    Question:
    If sinh x = 3/4, find the values of the other hyperbolic functions at x.

    I have tried solving it using terms of the e^x definitions, and also working through cosh^2 (x) - sinh^2 (x) = 1, but I am not getting anywhere. I'm not sure what to do now, or how much help anyone can give me...

    Thanks for reading and posting earlier, any further advice would be wonderful!

    cheers
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  7. #7
    Member Ruun's Avatar
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    \cosh^2(x)-\sinh^2(x)=1. It is given that \sinh(x)=\frac{3}{4}, plugging in, into the first equation, will give you the \cosh(x). The last thing you have to known, is that, as an equivalent of Euclidean trigonometry \frac{\sinh(x)}{\cosh(x)}=\tanh(x).
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  8. #8
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by klooless View Post
    Thank you to Ruun, flyingsquirrel and Craig for giving me tips to solve;

    Question:
    If sinh x = 3/4, find the values of the other hyperbolic functions at x.

    I have tried solving it using terms of the e^x definitions, and also working through cosh^2 (x) - sinh^2 (x) = 1, but I am not getting anywhere. I'm not sure what to do now, or how much help anyone can give me...

    Thanks for reading and posting earlier, any further advice would be wonderful!

    cheers
    sinhx= \frac{3}{4}

    \frac{e^x - e^{-x} }{2} = \frac{3}{4}

    e^x - e^{-x} = \frac{3}{2}

    e^{2x} - 1 = \frac{3e^x}{2} by multiply with  e^x

    e^{2x} -\frac{3e^x}{2} - 1 = 0

    let t= e^x

    t^2 - \frac{3t}{2} - 1 = 0

    t=\frac{ \frac{3}{2} \pm \sqrt{ \frac{9}{4} - 4(1)(-1) } } {2}

    t=\frac{ \frac{3}{2} \pm \sqrt{ \frac{25}{4} } } {2}

    e^x = \frac{\frac{3}{2} + \frac{5}{2} } {2}

    or

    e^x = \frac{\frac{3}{2} - \frac{5}{2} } {2}

    I think it clear right

    Editedpps I think you want the value of x anyway the others answer you
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  9. #9
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    Thank you :ddd

    Runn - that really cleared it up nicely for me, thanks for spelling it out!

    Amer - Super clear explanation, not exactly what this question asked for, but it helped with some other problems! Thanks!

    Cheers!
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