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, 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)

    Christianity as an organized religion has not always had a harmonious relationship with the family. Unlike Judaism, it kept almost no rituals that took place in private homes. The esteem that monasticism and priestly celibacy enjoyed implied a denigration of marriage and parenthood.
    Beatrice Gottlieb, U.S. historian. The Family in the Western World from the Black Death to the Industrial Age, ch. 12, Oxford University Press (1993)

    Morality and its victim, the mother—what a terrible picture! Is there indeed anything more terrible, more criminal, than our glorified sacred function of motherhood?
    Emma Goldman (1869–1940)