1. MTH 252 Integral Calculus Chapter 7 – Applications of the Definite Integral Section 7.9 – Hyperbolic Functions and Hanging Cables Copyright © 2005 by Ron Wallace, all rights reserved.

2. Reminder: The Circular Functions 1 Unit Circle: a 2 + b 2 = 1 x (a, b) x

3. Euler’s Formula NOTE: This will be proved in MTH 253. This identity implies that … What functions do you get if you remove the i ’s?

4. Hyperbolic Functions If a = coshx and b = sinhx, then any ordered pair ( a,b ) will be a point on the unit hyperbola: a 2 - b 2 =1. Also:

5. Hyperbolic Functions

6. Hyperbolic Functions: Derivatives

7. Inverse Hyperbolic Functions See page 512 formula 25. See page 512 formula 24. See page 512 formula 26.