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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.

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

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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?

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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:

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Hyperbolic Functions

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Hyperbolic Functions: Derivatives

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

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