Hyperbolic Functions

Hyperbolic functions are similar to trigonometric functions, but are defined in terms of exponentials. There are three fundamental hyperbolic functions: sinh, cosh and tanh:

Similarly, the reciprocal of each function exists:

Hyperbolic Graphs

For any value of x, sinh(-x) = -sinh(x)

• y = sinh(x) has no asymptotes

For any value of x, cosh(-x) = -cosh(x)

• y = cosh(x) never goes below y=1

• y = tanh(x) has asymptotes at y = ±1, and always stays between these

Inverse Hyperbolic Functions

Just like sin, cos and tan, the hyperbolic functions have inverses, arcsinh, arcosh and artanh:

The graphs of these are their respective reflections in the line y=x: