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  2. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/.../Inverse_trigonometric_functions

    The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x), arctan(x), etc. [1] (This convention is used throughout this article.) This notation arises from the following geometric relationships: [ citation needed ] when measuring in radians, an angle of θ radians will correspond to an arc ...

  3. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    atan2(y, x) returns the angle θ between the positive x-axis and the ray from the origin to the point (x, y), confined to (−π, π].Graph of ⁡ (,) over /. In computing and mathematics, the function atan2 is the 2-argument arctangent.

  4. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    The argument to the hyperbolic functions is a hyperbolic angle measure. 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 ...

  5. List of common coordinate transformations - Wikipedia

    en.wikipedia.org/wiki/List_of_common_coordinate...

    This means that the inverse function will only give values in the domain of the function, but restricted to a single period. Hence, the range of the inverse function is only half a full circle. Note that one can also use r = x 2 + y 2 θ ′ = 2 arctan ⁡ y x + r {\displaystyle {\begin{aligned}r&={\sqrt {x^{2}+y^{2}}}\\\theta '&=2\arctan ...

  6. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  7. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    A common example of a sigmoid function is the logistic function, which is defined by the formula: [1] ... another is the arctan function, ...

  8. List of integrals of inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    There are three common notations for inverse trigonometric functions. The arcsine function, for instance, could be written as sin −1, asin, or, as is used on this page, arcsin. For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions.

  9. List of integrals of inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    For a complete list of integral formulas, see lists of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration . For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions .

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