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  2. Music and mathematics - Wikipedia

    en.wikipedia.org/wiki/Music_and_mathematics

    Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory.

  3. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Pythagorean trigonometric identity. The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions. The identity is.

  4. 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.

  5. 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.

  6. Isaac Todhunter - Wikipedia

    en.wikipedia.org/wiki/Isaac_Todhunter

    Burney prize. Scientific career. Fields. Mathematics. Academic advisors. William Hopkins. Isaac Todhunter FRS (23 November 1820 – 1 March 1884), was an English mathematician who is best known today for the books he wrote on mathematics and its history.

  7. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    v. t. e. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has where e is the base of the natural logarithm, i is the imaginary ...

  8. Outline of trigonometry - Wikipedia

    en.wikipedia.org/wiki/Outline_of_trigonometry

    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. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical ...

  9. Trigonometric polynomial - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_polynomial

    Trigonometric polynomial. In the mathematical subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin (nx) and cos (nx) with n taking on the values of one or more natural numbers. The coefficients may be taken as real numbers, for real-valued functions.