# Hyperbolic functions at x

## Homework Statement

find all other hyperbolic function at x for tanhx=12/13

## Homework Equations

tanhx = sinhx/coshx
cothx=1/tanhx
etc...

## The Attempt at a Solution

the only thing i got is cothx=13/12
all i need to know is how to find sinhx and i will be fine.

Related Calculus and Beyond Homework Help News on Phys.org
Why not solve for x and then evaluate sinh(x)?

Why not solve for x and then evaluate sinh(x)?
so x= tanh-1(12/13) ?
then plug it in sinh(x)?

i am not sure if i get it..

Dick
Homework Helper
tanh(x)=sinh(x)/cosh(x)=12/13. cosh(x)^2-sinh(x)^2=1. That's two equations in two unknowns. Can you find the solution?

$$\tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} = \frac{e^{2x} - 1}{e^{2x} + 1}} = \frac{12}{13}$$
You can solve for x then plug it into the other hyperbolic trig functions. Or try what Dick suggested, looks like it should be easier.

yeah i asked a teacher today too and he explained the same thing.
that makes sense.

even though, tanhx = sinhx/coshx = 12/13 then from here i could use sinhx =12 and coshx = 13 right away..
but thats "the cheating way" i guess..

thanks for help!

Dick