Question

If tanh(x) = 4/5, how do you find the values of the other hyperbolic functions at x?

Answer 1

`sinhx=4/3`, `coshx=5/3`, `tanhx=4/5`
`cothx=5/4`, `sechx=3/5`, `cothx=5/4`

Explanation:

As `tanh^2x+sech^2x=1` and `tanhx=4/5`

hence `sechx=sqrt(1-(4/5)^2)=3/5`

and `coshx=1/sechx=5/3`

`cothx=1/tanhx=5/4`

`sinhx=tanhx*coshx=4/5*5/3=4/3`

`cschx=1/sinhx=3/4`