Hyperbolic Trigonometric Functions

Definitions

Hyperbolic functions are functions with similar properties to Trigonometric Functions but are defined in terms of exponentials. They are derived from by splitting into even and odd functions. With

Their relation from the trig functions comes form the fact that is connected to to the trig functions for complex . We can see the similarity between identities.

And we can get a very fundamental connection between the trig functions, Complex Numbers and the hyperbolics with

Like the trig functions we define 4 other functions as follows

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Inverse Hyperbolic Functions

Hyperbolic function	Inverse	Natural Log Form
	,

Identities and Equations

Generally given a trig identity you can find the corresponding hyperbolic identity with Osborn’s Rule

This only works for identities contain linear combinations of it works by substituting .

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Derivatives

Integration