Hyperbolic cosine. An exponential function of e and its argument ("cosh(x)"). Pronounced as it looks, like gosh. Exact function is as follows:

**
cosh(x) = (e**^{x}+e^{-x})/2

The hyperbolic trigonometric functions are called so because of the relationship between cosh(x) and sinh(x):

**cosh**^{2}(t)-sinh^{2}(t)=1

If we use x=cosh(t) and y=sinh(t), then we have the formula for an hyperbola in the plane. Compare this to the relationship between sin and cos:

**cos**^{2}(t)+sin^{2}(t)=1

which is the formula for a circle, using x=cos(t) and y=sin(t). One of the big bonuses of having functions like cosh and sinh available is that they have most of the same (or highly similar) properties as sin and cos do, but they sometimes provide a different perspective on a given problem.

See also: sinh, tanh, etc., which are hyperbolic sine and tangent respectively. Note that `cosh(x)=cos(i*x)`.