7.3 HW Problems

Table of Contents:

Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses

• The hyperbolic functions are formed by taking the combinations of the functions of $e^x$ and $e^{-x}$

Definitions and Identities

• The hyperbolic sine and hyperbolic cosine are defined by the equations:

$$ \sinh(x)=\frac{e^x-e^{-x}}{2} $$

$$ \cosh(x)=\frac{e^x+e^{-x}}{2} $$

• From this basic pair, the other hyperbolic functions (tangent, cotangent, secant, and cosecant) are defined.

The 6 Basic Hyperbolic Functions

Identities for Hyperbolic Functions

The identities are proved DIRECTLY from the definitions.

Derivatives and Integrals of Hyperbolic Functions