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  2. 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.

  3. Inverse trigonometric functions - Wikipedia

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

    The notations sin −1 (x), cos −1 (x), tan1 (x), etc., as introduced by John Herschel in 1813, [7] [8] are often used as well in English-language sources, [1] much more than the also established sin [−1] (x), cos [−1] (x), tan [−1] (x) – conventions consistent with the notation of an inverse function, that is useful (for example ...

  4. Law of tangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_tangents

    In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.

  5. Outline of trigonometry - Wikipedia

    en.wikipedia.org/wiki/Outline_of_trigonometry

    The following outline is provided as an overview of and topical guide to trigonometry: . Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles.

  6. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent. [2] Leonhard Euler used it to evaluate the integral ∫ d x / ( a + b cos ⁡ x ) {\textstyle \int dx/(a+b\cos x)} in his 1768 integral calculus textbook , [ 3 ] and Adrien-Marie Legendre described ...

  7. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    The function e (−1/x 2) is not analytic at x = 0: the Taylor series is identically 0, although the function is not. If f ( x ) is given by a convergent power series in an open disk centred at b in the complex plane (or an interval in the real line), it is said to be analytic in this region.

  8. 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 tan1 / 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 ...

  9. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    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.