Hyperbolic functions

**Kasper** · September 15th 2009, 01:02 PM

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?

**redsoxfan325** · September 15th 2009, 01:09 PM

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?

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

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

**Kasper** · September 15th 2009, 01:19 PM

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!

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