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

Question

29769 views around the world

You can reuse this answer
Creative Commons License

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#