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.

In this short lesson, you will learn about Tanh hyperbolic function and its properties including tanh function, tanh calculator, tanh formula, and tanh equation. You can see the graphical representation of the Tanh function in the image below.

$\text{tanh} (x + k\pi i) = \text{tanh}\ x$ $\text{coth} (x + k\pi i) =\text{coth} x$ Relationship between inverse hyperbolic and inverse trigonometric functions

tanh (z) = -i tan (iz) coth (z) = i cot (iz)

Hyperbolic tangent "tanh" (pronounced "than"): tanh(x) = sinh(x) cosh(x) = e x − e-x e x + e-x. tanh vs tan . Hyperbolic cotangent: coth(x) = cosh(x) sinh(x) = e x + e-x e x − e-x . Hyperbolic secant: sech(x) = 1 cosh(x) = 2 e x + e-x . Hyperbolic cosecant "csch" or "cosech": csch(x) = 1 sinh(x) = 2 e x − e-x. Why the Word "Hyperbolic" ?

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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.

This tanh calculator is the ultimate tool you need to deal with the hyperbolic tangent function! In what follows, we will explain what tanh is in math and how to calculate both the inverse and the derivative of tanh. We won't forget to give you extra tips on how to use this hyperbolic tangent calculator most efficiently. Let's go!

Tanh is the hyperbolic tangent function, which is the hyperbolic analogue of the Tan circular function used throughout trigonometry. Tanh [ α ] is defined as the ratio of the corresponding hyperbolic sine and hyperbolic cosine functions via .

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.