tanh is a hyperbolic function. tanh = sinh/cosh . The hyperbolic functions are
cosh (x) = {e^x + e^(-x)} /2
and sinh (x) = {e^x - e^(-x)} /2
{For info, the function cosh(x) describes a curve called a catenary,which is the shape that a chain makes when you hold it at both ends. }
What makes the hyperbolic functions different from the circular functions (that is, ordinary trig functions like sin and cos) is that they don't have complex components.
