Hyperbolic & Inverse Hyperbolic Functions

1. Hyperbolic & Inverse Hyperbolic Functions Lesson 7.8

2. Catenary Curve • The curve formed by a hangingcable 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: domainis 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