If coshx = (5/3) and x>0, how do you find the values of other hyperbolic functions at x?

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Answer 1 · 2016-07-24T17:28:39

#sinhx=+-4/3#, #sechx=3/5#, #cschx=+-3/4#, #tanhx=+-4/5# and #cothx=+-5/4#

Relation between #sinhx x# and #coshx# is given by

#cosh^2x-sinh^2x=1# and hence

#sinhx=sqrt(cosh^2x-1)=sqrt((5/3)^2-1)#

= #sqrt(25/9-1)=sqrt(16/9)=+-4/3#

#sechx=1/coshx=1/(5/3)=3/5#

#cschx=1/sinhx=1/(+-4/3)=+-3/4#

#tanhx=sinhx/coshx=(+-4/3)/(5/3)=+-4/5#

#cothx=1/tanhx=1/(+-4/5)=+-5/4#