Hyperbolic & Inverse Hyperbolic Functions

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Presentation transcript:

Hyperbolic & Inverse Hyperbolic Functions Lesson 7.8

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

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

Differentiation Rules for differentiating hyperbolic functions Note others on pg 483

Integration Formulas for integration

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

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'

Integrals Involving Inverse Hyperbolic Functions

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

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?

Assignment Lesson 7.8 Page 486 Exercises 1 – 45 odd