When hyperbolic function keys are not available on a calculator, it is still possible to evaluate the inverse hyperbolic functions by expressing them as logarithms, as shown here.

Use the formulas in the box here to express the numbers in terms of natural logarithms.

coth^-1 (5/4)

sinh'x = In(x + x + 1), coshx = In (x + x - 1), 1 + x 1 - x' 1 + tanh1x = 1/10/ In sech x csch"x = In ( ++* x 1 |x| coth x = In V1 - x X x + 1 x - 1 In - < x 1