If $tanhx=12/13$ , how do you find the values of the other hyperbolic functions at x?

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Answer 1 · 2016-09-18T08:10:34

$sinhx=+-12/5$ , $coshx=+-13/5$ , $cothx=13/12$ , $sechx=+-5/13$ and $cschx=+-5/12$

We can use relations between hyperbolic functions to find them.

As $sech^2x=1-tanh^2x$

$sech^2x=1-(12/13)^2=1-144/169=(169-144)/169=25/169$

or $sechx=+-5/13$

$coshx=1/sechx=+-13/5$

Hence $sinhx=tanhx xx coshx=+-12/13xx13/5=+-12/5$

and $cschx=1/sinhx=+-5/12$

$cothx=1/tanhx=13/12$

If tanhx=12/13tanhx=12/13, how do you find the values of the other hyperbolic functions at x?