In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

Oct 3, 2024 · Tanh (Hyperbolic Tangent): S-shaped function like sigmoid, but maps input values between -1 and 1. ReLU (Rectified Linear Unit): Maps input values to the maximum of 0 and the input value, introducing sparsity and reducing the likelihood of vanishing gradients.

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The graphs and properties such as domain, range and asymptotes of the 6 hyperbolic functions: sinh (x), cosh (x), tanh (x), coth (x), sech (x) and csch (x) are presented.

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TANH (x) returns the hyperbolic tangent of the angle x. The argument x must be expressed in radians. To convert degrees to radians you use the RADIANS function. The hyperbolic tangent can be defined as: tanh(x) = sinh(x) cosh(x) tanh (x) = sinh (x) cosh (x) where sinh is the hyperbolic sine function and cosh is the hyperbolic cosine function.

Y = tanh(X) returns the hyperbolic tangent of the elements of X. The tanh function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians.

Here are two graphics showing the real and imaginary parts of the hyperbolic tangent function over the complex plane. For real values of argument , the values of are real. In the points , the values of are algebraic. In several cases, they can be , 0, or ⅈ:

Sep 10, 2020 · The tanh function involves two functions, sinh x divided by cosh x. This animation illustrates this: When x is zero, sinh x is 0 and cosh x is 1, so the result is 0. As x gets larger, as the animation shows, sinh x and cosh x become ever closer is value, although sinh x is always slightly smaller. The value of tanh x therefore tends towards 1.

Plot of the hyperbolic tangent. tanh (x) goes to +/- 1 for x to +- infinity while it is approximately linear for abs (x) < 1. Appears in many places in physics, e.g. in the magnetization of an ideal paramagnet of independent spins.