1. Hyperbolic Functions Who Needs Them?
Chapter 6.9

2. The gentle arc of a suspension bridge or the
complex geometry of Einstein’s
Theory of Relativity provide us with real-life
examples of Hyperbolic Functions!

3. Basic Definitions…
The hyperbolic functions are built out of the exponential function:
We can form other hyperbolic functions:

4. Contrasting Circular Functions with Hyperbolic Functions
Sine and Cosine are bounded, periodic functions
Sinh and Cosh are unbounded
Sine and Cosine are related to the UNIT CIRCLE – Hyperbolic functions are related to the UNIT HYPERBOLA!

5. Review Identities Pg 165 – Basic Relations
Pg Derivative Patterns

6. Compare and Contrast
The hyperbolic functions, their inverses and derivatives often appear very similar to the circular functions (sin, cos etc)…
So – how do I remember all this stuff?
You don’t! Just be sure to understand that these are a new set of functions with some important similarities and differences with the ordinary circular functions. You will learn some of the easier patterns but in general it is fair to rely on Tables or Computer Algebra Systems.

7. Samples…
Pg 167: 7, 11, 17, 21, 31