mathematics, a trigonometric substitution replaces a trigonometric function for another expression. In calculus, trigonometric substitutions are a technique...

tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions of x...

In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals...

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...

mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential...

used the identities for the trigonometric functions of sums and differences of angles in terms of the products of trigonometric functions of those angles...

tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas...

half-angle substitution Trigonometric integral Trigonometric substitution Applications Fourier transform Wave equation For examples of trigonometric functions...

method Integration by substitution Tangent half-angle substitution Differentiation under the integral sign Trigonometric substitution Partial fractions in...

The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change...

of trigonometric series. History of science portal Mathematics portal Greek mathematics History of mathematics Trigonometric functions Trigonometry Ptolemy's...

trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions...

trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions...

function. Mathematics portal Integration by substitution Trigonometric substitution Weierstrass substitution N. Piskunov, Diferentsiaal- ja integraalarvutus...

In trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle. The tangent of half...

closed under arithmetic operations, every trigonometric number is algebraic. The minimal polynomials of trigonometric numbers can be explicitly enumerated...

matrices, and various Banach algebras. Polar/Trigonometric forms of hypercomplex numbers Polygonometry – trigonometric identities for multiple distinct angles...

involving the inverse trigonometric functions. For a complete list of integral formulas, see lists of integrals. The inverse trigonometric functions are also...

(antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals...

\{B_{n}\}} are coefficients. It is an infinite version of a trigonometric polynomial. A trigonometric series is called the Fourier series of the integrable...

digital computer, is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions...

textbooks of astronomy and trigonometry and a treatise that was never published: Harmonicon coeleste. In 1579, the trigonometric tables Canon mathematicus...

include rational and exponential functions, logarithm, trigonometric functions and inverse trigonometric functions, and the operations of multiplication and...

may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of complex...

require using a different trigonometric form. To illustrate, let us assume we had available seven-place logarithm and trigonometric tables, and wished to...

A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable...

of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a...

traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations...

versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Aryabhatia, Section I) trigonometric tables. The versine of an...

{n}}]}e^{-x^{2}}dx\leq 2{\sqrt {n}}\int _{[0,1]}(1+x^{2})^{-n}dx} By trigonometric substitution, we exactly compute those two bounds: 2 n ( 2 n ) ! ! / ( 2 n...