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  1. #1
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    Help on hyperbolic functions

    Even after taking calculus, I've not learned hyperbolic functions, which leads me to believe that it's a relatively minor part of mathematics. Nevertheless, I want to learn them. Now, after googling for a while, I've gotten a general idea of what hyperbolic functions stand for but I still need some clarification.

    (1.)Let's take sinh(x). Does "x" represent angle, either degree or radian? Or something else?

    (2.) Why does the graph of sinh(x) go to infinity if it doesn't even reach one (to my limited knowledge, of course). I mean, if you look at the unit hyperbola and use the trig sin, you'll see that the sine ratio never exceeds 1. I'm sure I'm missing something here.

    (3.) What is the general domain of hyperbolic functions? I mean, for standard trig, it's nonexistent (because it'll go in circles) but what about hyperbolic functions? It's difficult to visualize the domain for a split-up graph like a hyperbola.

    etc., etc., etc... I'd just appreciate some solid instruction regarding hyperbolic functions. They're not found in my textbook and the internet sucks at clarification.

    I wasn't sure if this calculus section was the appropriate place to post because I don't know where hyperbolic functions belong. I'm sorry if it doesn't belong to this calculus section.
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    Quote Originally Posted by Kaitosan View Post
    Even after taking calculus, I've not learned hyperbolic functions, which leads me to believe that it's a relatively minor part of mathematics. Nevertheless, I want to learn them. Now, after googling for a while, I've gotten a general idea of what hyperbolic functions stand for but I still need some clarification.

    (1.)Let's take sinh(x). Does "x" represent angle, either degree or radian? Or something else?

    (2.) Why does the graph of sinh(x) go to infinity if it doesn't even reach one (to my limited knowledge, of course). I mean, if you look at the unit hyperbola and use the trig sin, you'll see that the sine ratio never exceeds 1. I'm sure I'm missing something here.

    (3.) What is the general domain of hyperbolic functions? I mean, for standard trig, it's nonexistent (because it'll go in circles) but what about hyperbolic functions? It's difficult to visualize the domain for a split-up graph like a hyperbola.

    etc., etc., etc... I'd just appreciate some solid instruction regarding hyperbolic functions. They're not found in my textbook and the internet sucks at clarification.

    I wasn't sure if this calculus section was the appropriate place to post because I don't know where hyperbolic functions belong. I'm sorry if it doesn't belong to this calculus section.
    turns out x is a real or complex number as Plato sai

    Hyperbolic functions can also be written in terms of exponential functions

    sinh(x) = \frac{e^x - e^{-x}}{2}

    cosh(x) = \frac{e^x + e^{-x}}{2}

    tanh(x) = \frac{sinh(x)}{cosh(x)} = {e^{2x}-1}{e^{2x}+1}

    (and so on for the reciprocals of these). In sinh(x) if the numerator is greater than two then it will exceed one. The domain would also be all the real numbers in all three of these.
    Last edited by e^(i*pi); May 11th 2009 at 10:57 AM.
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    Quote Originally Posted by e^(i*pi) View Post
    x is an angle and any angle measure is fine.

    Hyperbolic functions can also be written in terms of exponential functions

    sinh(x) = \frac{e^x - e^{-x}}{2}

    cosh(x) = \frac{e^x + e^{-x}}{2}

    tanh(x) = \frac{sinh(x)}{cosh(x)} = {e^{2x}-1}{e^{2x}+1}

    (and so on for the reciprocals of these). In sinh(x) if the numerator is greater than two then it will exceed one. The domain would also be all the real numbers in all three of these.
    It doesn't make sense for x to be written in terms of angle though because then sinh(x) will have to be negative sometimes but it's always positive for x > 0.
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    Quote Originally Posted by Kaitosan View Post
    It doesn't make sense for x to be written in terms of angle though because then sinh(x) will have to be negative sometimes but it's always positive for x > 0.
    x is never written in terms of angle .
    x is a real or complex number
    PERIOD! End of story.
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