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:

    Women, because of their colonial relationship to men, have to fight for their own independence. This fight for our own independence will lead to the growth and development of the revolutionary movement in this country. Only the independent woman can be truly effective in the larger revolutionary struggle.
    Women’s Liberation Workshop, Students for a Democratic Society, Radical political/social activist organization. “Liberation of Women,” in New Left Notes (July 10, 1967)

    Henry David Thoreau, who never earned much of a living or sustained a relationship with any woman that wasn’t brotherly—who lived mostly under his parents’ roof ... who advocated one day’s work and six days “off” as the weekly round and was considered a bit of a fool in his hometown ... is probably the American writer who tells us best how to live comfortably with our most constant companion, ourselves.
    Edward Hoagland (b. 1932)

    Literature does not exist in a vacuum. Writers as such have a definite social function exactly proportional to their ability as writers. This is their main use.
    Ezra Pound (1885–1972)