Hyperbolic Function - Relationship To The Exponential Function

Relationship To The Exponential Function

From the definitions of the hyperbolic sine and cosine, we can derive the following identities:

and

These expressions are analogous to the expressions for sine and cosine, based on Euler's formula, as sums of complex exponentials.

Read more about this topic:  Hyperbolic Function

Famous quotes containing the words relationship to the, relationship to, relationship and/or function:

    Film music should have the same relationship to the film drama that somebody’s piano playing in my living room has to the book I am reading.
    Igor Stravinsky (1882–1971)

    Film music should have the same relationship to the film drama that somebody’s piano playing in my living room has to the book I am reading.
    Igor Stravinsky (1882–1971)

    The relationship between mother and professional has not been a partnership in which both work together on behalf of the child, in which the expert helps the mother achieve her own goals for her child. Instead, professionals often behave as if they alone are advocates for the child; as if they are the guardians of the child’s needs; as if the mother left to her own devices will surely damage the child and only the professional can rescue him.
    Elaine Heffner (20th century)

    The intension of a proposition comprises whatever the proposition entails: and it includes nothing else.... The connotation or intension of a function comprises all that attribution of this predicate to anything entails as also predicable to that thing.
    Clarence Lewis (1883–1964)