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De Moivre's Theorem for Trig Identities by Michael Croucher, Wolfram Demonstrations Project Listen to this article ( 18 minutes ) This audio file was created from a revision of this article dated 5 June 2021 ( 2021-06-05 ) , and does not reflect subsequent edits.
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 .
Geometry is used extensively in trigonometry. Angle – the angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane.
Chebyshev polynomials can be defined in this form when studying trigonometric polynomials. [4] That cos nx is an n th-degree polynomial in cos x can be seen by observing that cos nx is the real part of one side of de Moivre's formula: + = ( + ).
De Gua's theorem ; De Moivre's theorem (complex analysis) De Rham's theorem (differential topology) Deduction theorem ; Dehn-Nielsen-Baer theorem (geometric topology) Denjoy theorem (dynamical systems) Denjoy–Carleman theorem (functional analysis) Denjoy-Young-Saks theorem (real analysis) Desargues's theorem (projective geometry)
de Moivre's formula, a trigonometric identity; Theorem of de Moivre–Laplace, a central limit theorem This page was last edited on 28 December 2019, at 06:07 (UTC). ...
The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six trigonometric functions of θ are, for angles smaller than the right angle:
Abraham de Moivre was born in Vitry-le-François in Champagne on 26 May 1667. His father, Daniel de Moivre, was a surgeon who believed in the value of education. Though Abraham de Moivre's parents were Protestant, he first attended the Christian Brothers' Catholic school in Vitry, which was unusually tolerant given religious tensions in France at the time.