hyperbolic function?

Question

if sinh x = 3\2 find exact values for cosh x and tanh x

Answer 1

cosh^2(x) - sinh^2(x) = 1
Therefore for your x:

cosh(x)
= +/-sqrt(1 + 9/4)
= +/-sqrt(13) / 2

tanh(x)
= sinh(x) / cosh(x)
= +/-(3/2)(2sqrt(13) / 13)
= +/-3sqrt(13)/13.

Answer 2

cosh^2x-sinh^2x =1
so cosh^2x= 1+9/4 = 13/4 and cosh x= 1/2 sqrt(13)
tanh x= sinh /cosh = 3/2*2/sqrt(13) =3sqrt(13)/13
Additional As cos h x= 1/2(e^x+e^-x) it takes only positive values