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) = -coth x. \displaystyle \text {sinh} (x \pm y) = \text {sinh}\ x \ \text {cosh}\ y \pm \text {cosh}\ x\ \text {sinh}\ y sinh(x±y) = sinh x cosh y ±cosh x sinh y. \displaystyle \text {cosh} (x …

Feb 6, 2021 · Equation and graph The coth function is the reciprocal of the tanh function, and is only defined for non-zero values: coth x = 1 t a n h x = cosh x sinh x (This is analogous with trig functions, where cot is the reciprocal of tan.) Substituting the formula for tanh gives: coth x = e x + e − x e x − e − x Here is a graph of the function:

In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent.

Nov 25, 2024 · The hyperbolic cotangent function (coth) is the reciprocal of the hyperbolic tangent function, which is given by the expression: coth x = 1 tanh x = e x + e − x e x − e − x. Now, on graphing the hyperbolic cotangent function y = coth x, we get. Here is the summary of all graphs of the hyperbolic functions:

Coth is a mathematical function that is used in various areas of mathematics, including calculus, trigonometry, and algebra. It is the hyperbolic cotangent function, which is defined as the ratio …

The function coth (x) is the hyperbolic cotangent function. It is defined as the ratio of the hyperbolic cosine to the hyperbolic sine of a given angle x.

The domain of coth coth and csch csch is x ≠ 0 x ≠ 0 while the domain of the other hyperbolic functions is all real numbers. Graphs are shown in Figure 3.11.1 3.11. 1

Learn Hyperbolic Trig Identities and other Trigonometric Identities, Trigonometric functions, and much more for free. Download Hyperbolic Trig Worksheets.

As a hyperbolic function, hyperbolic cotangent is usually abbreviated as "coth", as in the following equation: \coth (\theta) coth(θ) If you already know the hyperbolic cotangent, use the inverse hyperbolic cotangent or arccoth to find the angle. After, see the hyperbolic functions and inverse hyperbolic functions in two convenient tools.