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  2. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    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. List of trigonometric identities - Wikipedia

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

    When the direction of a Euclidean vector is represented by an angle , this is the angle determined by the free vector (starting at the origin) and the positive -unit vector. The same concept may also be applied to lines in a Euclidean space, where the angle is that determined by a parallel to the given line through the origin and the positive x ...

  4. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    A ray through the unit hyperbola = in the point (,), where is twice the area between the ray, the hyperbola, and the -axis. The earliest and most widely adopted symbols use the prefix arc-(that is: arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth), by analogy with the inverse circular functions (arcsin, etc.).

  5. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    In the integral , we may use = ⁡, = ⁡, = ⁡. Then, = ⁡ ⁡ = ⁡ (⁡) = ⁡ ⁡ = = + = ⁡ +. The above step requires that > and ⁡ > We can choose to be the principal root of , and impose the restriction / < < / by using the inverse sine function.

  6. 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.

  7. Arctangent series - Wikipedia

    en.wikipedia.org/wiki/Arctangent_series

    In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function: [1] ⁡ = + + = = + +. This series converges in the complex disk | |, except for = (where =).

  8. List of integrals of inverse trigonometric functions - Wikipedia

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

    The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.For a complete list of integral formulas, see lists of integrals.

  9. Tangent half-angle formula - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle_formula

    The sides of this rhombus have length 1. The angle between the horizontal line and the shown diagonal is ⁠ 1 / 2 ⁠ (a + b).This is a geometric way to prove the particular tangent half-angle formula that says tan ⁠ 1 / 2 ⁠ (a + b) = (sin a + sin b) / (cos a + cos b).