1. ## 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?

2. 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 $\frac{3}{4}=\frac{e^t - e^{-t}}{2}$, 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?
$\cosh^2(x)-\sinh^2(x)=1$

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

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

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