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.

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$\text{cosh} (x + 2k \pi i) = \text{cosh}\ x$ $\text{sech} (x + 2k\pi i) = \text{sech} x$ $\text{tanh} (x + k\pi i) = \text{tanh}\ x$ $\text{coth} (x + k\pi i) =\text{coth} x$ Relationship between inverse hyperbolic and inverse trigonometric functions

Graphs of Hyperbolic Functions. 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 : \( \sinh(x) = \dfrac{e^x - e^{-x}}{2} \)

5 天之前 · The hyperbolic secant is defined as sechz = 1/(coshz) (1) = 2/(e^z+e^(-z)), (2) where coshz is the hyperbolic cosine. It is implemented in the Wolfram Language as Sech[z]. On the real line, it has a maximum at x=0 and inflection points at x=+/-cosh^(-1)(sqrt(2))=0.8813735... (OEIS A091648). It has a fixed point at x=0.76500995... (OEIS A069814).

SECH (x) returns the hyperbolic secant 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 SECH function applied to all elements.

2024年11月25日 · Similarly, the hyperbolic secant function (sech) is the reciprocal of the hyperbolic cosine function, which is given by the expression: sech x = 1 cosh x = 2 e x + e − x. Now, on graphing the hyperbolic secant function y = sech x, we get.

2021年2月4日 · Here is a graph of the function: We can sketch the sech curve based on the cosh curve: The cosh curve tends to +∞ for large negative x, it has a value of 1 when x = 0, and it tends to +∞ for large positive x. The sech curve is the reciprocal of cosh.

The calculator will draw the graph of the function $$$ y = f{\left(x \right)} = \operatorname{sech}{\left(x \right)} $$$. To draw a parabola, circle, ellipse or hyperbola, choose the "Implicit" option.

The file contains 2 graphs - cosh(ax) and sech(ax) Discover Resources. Equations of tangents to a curve with given slope; Geogebra pg 126 25