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:

    Whatever may be our just grievances in the southern states, it is fitting that we acknowledge that, considering their poverty and past relationship to the Negro race, they have done remarkably well for the cause of education among us. That the whole South should commit itself to the principle that the colored people have a right to be educated is an immense acquisition to the cause of popular education.
    Fannie Barrier Williams (1855–1944)

    Sometimes in our relationship to another human being the proper balance of friendship is restored when we put a few grains of impropriety onto our own side of the scale.
    Friedrich Nietzsche (1844–1900)

    When any relationship is characterized by difference, particularly a disparity in power, there remains a tendency to model it on the parent-child-relationship. Even protectiveness and benevolence toward the poor, toward minorities, and especially toward women have involved equating them with children.
    Mary Catherine Bateson (20th century)

    The function of comedy is to dispel ... unconsciousness by turning the searchlight of the keenest moral and intellectual analysis right on to it.
    George Bernard Shaw (1856–1950)