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  2. Gudermannian function - Wikipedia

    en.wikipedia.org/wiki/Gudermannian_function

    Twice the area of the purple triangle is the stereographic projection s = tan ⁠ 1 / 2 ⁠ ϕ = tanh ⁠ 1 / 2 ⁠ ψ. The blue point has coordinates (cosh ψ, sinh ψ). The red point has coordinates (cos ϕ, sin ϕ). The purple point has coordinates (0, s). Graph of the Gudermannian function. Graph of the inverse Gudermannian function.

  3. Hyperbolic secant distribution - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_secant_distribution

    where "arctan" is the inverse (circular) tangent function. Johnson et al. (1995) [ 1 ] : 147 places this distribution in the context of a class of generalized forms of the logistic distribution , but use a different parameterisation of the standard distribution compared to that here.

  4. Involution (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Involution_(mathematics)

    An involution is a function f : X → X that, when applied twice, brings one back to the starting point. In mathematics, an involution, involutory function, or self-inverse function [1] is a function f that is its own inverse, f(f(x)) = x. for all x in the domain of f. [2] Equivalently, applying f twice produces the original value.

  5. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/.../Inverse_trigonometric_functions

    Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length , then applying the Pythagorean theorem and definitions of the trigonometric ratios.

  6. Your Grandmother Never Made This Pimiento Cheese Mistake, And ...

    www.aol.com/grandmother-never-made-pimiento...

    No, it’s not spelling “pimiento” wrong…

  7. Americans Spend $135 at the Airport: See the Top ... - AOL

    www.aol.com/finance/americans-spend-135-airport...

    The airport is full of spending temptations at every corner, and it’s easy to give into those temptations when you have time to kill before your flight. According to a recent survey from ...

  8. Sharp downgrades to US unit labor costs bode well for ...

    www.aol.com/news/us-third-quarter-unit-labor...

    Labor costs were previously reported to have advanced at a 2.4% rate in the April-June quarter. They increased at a 2.2% pace in the third quarter from a year ago, revised down from the previously ...

  9. Inverse curve - Wikipedia

    en.wikipedia.org/wiki/Inverse_curve

    In inversive geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle with center O and radius k the inverse of a point Q is the point P for which P lies on the ray OQ and OP·OQ = k 2. The inverse of the curve C is then the locus of P as Q runs over C.