# Thread: Help on hyperbolic functions

1. ## 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.

2. Originally Posted by Kaitosan
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.

3. Originally Posted by e^(i*pi)
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.

4. Originally Posted by Kaitosan
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.