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Math Help - Hyperbolic functions

  1. #1
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    Hyperbolic functions

    Hey folks! I've just learned about Hyperbolic functions, and I've got a question type here that I haven't seen done before if anyone could lend me a hint.

    If sinh(x)=\frac{3}{4}, find the value of the other hyperbolic functions at x.
    I must be having a bad math day, it seems like it should be easy, but I just can't figure out where to start. If I set \frac{3}{4}=\frac{e^t - e^{-t}}{2}, I'm not too sure where to go from there to see what cosh(x) is equal to short of solving for t which looks like a mess. I had a friend tell me to use trigonometric relationships (like that between cosine and sine), but I'm not so sure that this relationship works in the same way, does it?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Kasper View Post
    Hey folks! I've just learned about Hyperbolic functions, and I've got a question type here that I haven't seen done before if anyone could lend me a hint.

    I must be having a bad math day, it seems like it should be easy, but I just can't figure out where to start. If I set \frac{3}{4}=\frac{e^t - e^{-t}}{2}, I'm not too sure where to go from there to see what cosh(x) is equal to short of solving for t which looks like a mess. I had a friend tell me to use trigonometric relationships (like that between cosine and sine), but I'm not so sure that this relationship works in the same way, does it?
    \cosh^2(x)-\sinh^2(x)=1

    \tanh(x)=\frac{\sinh(x)}{\cosh(x)}
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  3. #3
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    Quote Originally Posted by redsoxfan325 View Post
    \cosh^2(x)-\sinh^2(x)=1

    \tanh(x)=\frac{\sinh(x)}{\cosh(x)}
    Woooow, I'm slow today. Thanks man!
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