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  2. Inverse trigonometric functions - Wikipedia

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

    A Riemann surface for the argument of the relation tan z = x. The orange sheet in the middle is the principal sheet representing arctan x. The blue sheet above and green sheet below are displaced by 2π and −2π respectively. Since the inverse trigonometric functions are analytic functions, they can be extended from the real line to the ...

  3. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics ...

  4. List of trigonometric identities - Wikipedia

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

    Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

  5. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    In computing and mathematics, the function atan2 is the 2- argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument (also called phase or angle) of the complex number (The argument of a function and the ...

  6. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Fourier. v. t. e. Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.

  7. Tangent half-angle formula - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle_formula

    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). The formulae sin ⁠ 1 2 ⁠(a + b) and cos ⁠ 1 2 ⁠(a + b) are the ratios of the actual distances to the length ...

  8. 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 =).

  9. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    t. e. In mathematics, a trigonometric substitution replaces a trigonometric function for another expression. In calculus, trigonometric substitutions are a technique for evaluating integrals. In this case, an expression involving a radical function is replaced with a trigonometric one.