tanhfunktsiooni

The tanh function, also known as the hyperbolic tangent function, is a mathematical function defined as the ratio of the hyperbolic sine (sinh) to the hyperbolic cosine (cosh). Mathematically, it is expressed as tanh(x) = sinh(x) / cosh(x), which further simplifies to tanh(x) = (e^x - e^-x) / (e^x + e^-x).

The tanh function maps any real number to a value between -1 and 1. Its output approaches -1 as the input approaches negative infinity, and it approaches 1 as the input approaches positive infinity. At an input of 0, the function's output is 0. This "S" shaped curve is a characteristic of the tanh function.

It is an odd function, meaning tanh(-x) = -tanh(x), and it is always increasing. The tanh function finds applications in various fields, particularly in machine learning and neural networks where it is used as an activation function. Its ability to compress values into a bounded range and its smooth, non-linear nature make it suitable for introducing non-linearity into models, aiding in the learning of complex patterns. It is also utilized in signal processing and in the study of differential equations.