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  2. Uses of trigonometry - Wikipedia

    en.wikipedia.org/wiki/Uses_of_trigonometry

    Various types of equations can be solved using trigonometry. For example, a linear difference equation or linear differential equation with constant coefficients has solutions expressed in terms of the eigenvalues of its characteristic equation; if some of the eigenvalues are complex, the complex terms can be replaced by trigonometric functions ...

  3. Field equation - Wikipedia

    en.wikipedia.org/wiki/Field_equation

    In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space.

  4. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. [2] The Greeks focused on the calculation of chords , while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions ) such as sine .

  5. List of trigonometric identities - Wikipedia

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

    An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

  6. De Moivre's formula - Wikipedia

    en.wikipedia.org/wiki/De_Moivre's_formula

    The formula is important because it connects complex numbers and trigonometry. By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos nx and sin nx in terms of cos x and sin x. As written, the formula is not valid for non-integer ...

  7. 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. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.

  8. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. 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.

  9. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...

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