Hyperbolic Functions
Table of Contents
$$\small \sinh(x) = \frac{e^x - e^{-x}}{2}, \cosh(x) = \frac{e^x + e^{-x}}{2}, \tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}$$
Where
- \(e\) is Euler’s number ~= 2.71828, and
- \(i\) is the imaginary unit, \(\sqrt{-1}\)
Complex trig definitions #
The hyperbolic functions can be defined in terms of the trig functions with complex arguments:
- \(\sinh(x) = -i \sin(ix)\)
- \(\cosh(x) = \cos(ix)\)
- \(\tanh(x) = -i \tan(ix)\)