Hyperbolic functions
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Hyperbolic Functions - The need for hyperbolic functions
Equations are omitted for technical reasons - download the original pdf
Suppose we hang a rope between two points, which are -1 and +1 units from a fixed point O. [Diagram goes here - download the original to see it.] It can be shown that y as a function of x is given by:- [Equation goes here - download the original to see it.] Where a is a constant. The constant a is determined by the length of the rope. [Diagram goes here - download the original to see it.] As a increases the curve becomes more bent. It turns out that in applications of the calculus to problems in physics and mechanics the expression [Equation goes here - download the original to see it.] recurs frequently. It, therefore, is appropriate to define a function that we can equate with this. In fact, we define six hyperbolic functions as follows.
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Contents of
Hyperbolic functions
1 Hyperbolic Functions - The need for hyperbolic functions
2 Definitions of the hyperbolic functions
3 Graphs of the hyperbolic functions
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