Hyperbolic functions

• Sep 15th 2009, 01:02 PM
Kasper
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.

Quote:

If $\displaystyle sinh(x)=\frac{3}{4}$, find the value of the other hyperbolic functions at $\displaystyle x$.
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 $\displaystyle \frac{3}{4}=\frac{e^t - e^{-t}}{2}$, I'm not too sure where to go from there to see what $\displaystyle cosh(x)$ is equal to short of solving for $\displaystyle t$ 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?
• Sep 15th 2009, 01:09 PM
redsoxfan325
Quote:

Originally Posted by Kasper
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 $\displaystyle \frac{3}{4}=\frac{e^t - e^{-t}}{2}$, I'm not too sure where to go from there to see what $\displaystyle cosh(x)$ is equal to short of solving for $\displaystyle t$ 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?

$\displaystyle \cosh^2(x)-\sinh^2(x)=1$

$\displaystyle \tanh(x)=\frac{\sinh(x)}{\cosh(x)}$
• Sep 15th 2009, 01:19 PM
Kasper
Quote:

Originally Posted by redsoxfan325
$\displaystyle \cosh^2(x)-\sinh^2(x)=1$

$\displaystyle \tanh(x)=\frac{\sinh(x)}{\cosh(x)}$

Woooow, I'm slow today. Thanks man! :)