1. Hyperbolic & Inverse Hyperbolic Functions
Lesson 7.8

2. Catenary Curve
The curve formed by a hanging cable is called a catenary
They behave similar to trig functions
They are related to the hyperbola in similar manner as trig functions to the circle
Thus are called hyperbolic functions

3. Hyperbolic Functions Definitions Note: domain is all real numbers
Note properties, Theorem 7.2, pg 482

4. Differentiation Rules for differentiating hyperbolic functions
Note others on pg 483

5. Integration
Formulas for integration

6. Example
Try
What should be the u, the du?
Substitute, integrate

7. Application
Electric wires suspended between two towers form a catenary with the equation
If the towers are 120 ft apart, what is the length of the suspended wire?
Use the arc length formula
120'

8. Integrals Involving Inverse Hyperbolic Functions

9. Try It! Note the definite integral What is the a, the u, the du?
a = 3, u = 2x, du = 2 dx

10. Application Find the area enclosed by x = -¼, x = ¼, y = 0, and
Which pattern does this match?
What is the a, the u, the du?

11. Assignment
Lesson 7.8
Page 486
Exercises 1 – 45 odd