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

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.

COTH (x) returns the hyperbolic cotangent of x. The argument x can be a real number or a matrix. When it is a matrix, the function returns a matrix with the same dimensions and with the COTH function applied to all elements.

Plot of the hyperbolic cotangent function y = cothx. Function codomain is entire real axis with gap in the middle: (−∞, −1)∪(1, +∞). 3. Identities. Base: coth 2 x − csch 2 x = 1. By definition: coth x ≡ cosh x /sinh x ≡ 1 /tanh x. Property of antisymmetry: coth− x = −coth x. Half-argument:

4 days ago · The hyperbolic cotangent is defined as cothz= (e^z+e^ (-z))/ (e^z-e^ (-z))= (e^ (2z)+1)/ (e^ (2z)-1). (1) The notation cthz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram Language as Coth [z].

Mathematical function, suitable for both symbolic and numerical manipulation. automatically evaluates to exact values when its argument is the (natural) logarithm of a rational number. When given exact numeric expressions as arguments, may be evaluated to arbitrary numeric precision.

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. The six hyperbolic functions are defined as follows: Hyperbolic Sine Function : \( \sinh(x) = \dfrac{e^x - e^{-x}}{2} \)

The right graphic is a contour plot of the scaled absolute value, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest. At the function has an essential singularity.

Contour plot of the real part (red) and imaginary part (blue) of over the . Here . By the Cauchy–Riemann equations the curves of constant real part and constant imaginary part are orthogonal.

Feb 6, 2021 · The coth function involves two functions, $\cosh{x}$ divided by $\sinh{x}$. This animation illustrates this: When $x$ is large and negative, $\sinh{x}$ becomes ever closer to $-\cosh{x}$.