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 and/or function:

    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 state’s one function is to give.
    The bud must bloom till blowsy blown
    Its petals loosen and are strown;
    And that’s a fate it can’t evade
    Unless ‘twould rather wilt than fade.”
    Robert Frost (1874–1963)