# Hyperbolic_functions.ppt - KFUPM HYPERBOLIC FUNCTIONS Stan Wagon riding his tricycle with square wheels (a mathematician at Macalester College in St. Paul)

HYPERBOLIC FUNCTIONS Definitions and Identities

HYPERBOLIC FUNCTIONS x e e

cosh( x) 2 x

x e e sinh( x) 2

x We pronounce cosh(x)

sinh(x) hyperbolic cosine

kosh x cinch x Example: Find cosh(0)

hyperbolic sine sinh(0)

HYPERBOLIC FUNCTIONS x e e cosh( x)

2 x x

e e sinh( x) 2

x HYPERBOLIC FUNCTIONS HYPERBOLIC FUNCTIONS

HYPERBOLIC FUNCTIONS In simple suspension bridges such as the Capilano Suspension Bridge, where the weight runs parallel to

8 the cables, the cables follow a catenary curve. HYPERBOLIC FUNCTIONS

HYPERBOLIC FUNCTIONS 093E2 11

093E2 12

F091 13 F092

HYPERBOLIC FUNCTIONS Derivatives of Hyperbolic

Functions HYPERBOLIC FUNCTIONS F083

F092 F093

F093 HYPERBOLIC FUNCTIONS Integrals of

Hyperbolic Functions HYPERBOLIC FUNCTIONS

HYPERBOLIC FUNCTIONS EXAMPLE: HYPERBOLIC FUNCTIONS

Inverse Hyperbolic Functions HYPERBOLIC FUNCTIONS

HYPERBOLIC FUNCTIONS HYPERBOLIC FUNCTIONS

HYPERBOLIC FUNCTIONS HYPERBOLIC FUNCTIONS HYPERBOLIC FUNCTIONS

Derivatives of Inverse Hyperbolic Functions

HYPERBOLIC FUNCTIONS F093

093E2 F091 34

HYPERBOLIC FUNCTIONS Integrals leads to Inverse

Hyperbolic Functions HYPERBOLIC FUNCTIONS

HYPERBOLIC FUNCTIONS EXAMPLE: 1

2dx 3 4x 0

2 38 39

40