Hyperbolic Functions (Introduction)

This tutorial video uses animations, graphs, and exponential definitions to give you an introduction to hyperbolic functions. We explain how hyperbolic trig functions are based on the unit hyperbola, in the same way that the circular functions are based on the unit circle. This hyperbolic functions introduction provides information about hyperbolic function identities and formulas for calculus. This is a common topic found in a Calculus 2 course.
0:00 Circular Trig Functions vs Hyperbolic Trig Functions
2:24 Using the unit hyperbola to develop functions
3:25 Hyperbolic sine and cosine functions
5:58 Exponential identities for sinh x and cosh x
7:42 Other hyperbolic functions
8:14 List of some applications

[Ensign_Cthulhu]

Can you defend the cosh and sinh functions being the average of the exponential functions algebraically at the high-school level, or does that require a much more advanced knowledge of mathematics?