Exact trigonometric values information

{\displaystyle \cos(\pi /4)={\sqrt {2}}/2} . While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a...

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

angles is given below. For more complex angle expressions see Exact trigonometric values § Common angles. 90 degree increments: Sine and cosine are used...

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

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

kernel Euler's formula Exact trigonometric values Exponential sum Trigonometric integral Trigonometric polynomial Trigonometric series Altern base Angle...

the square root of 2 added or subtracted, appears in several exact trigonometric values for angles at multiples of 15 degrees ( π / 12 {\displaystyle...

are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation...

Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic...

triangles which is commonly used in geometry classes to find the values of trigonometric functions of 15° and 75°. It is named after Douglas S. Ailles who...

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

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

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

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

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

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

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

astronomy and mathematics suggest that he found the Taylor series for the trigonometric functions of sine, cosine, and arctangent (see Madhava series). During...

}}={\frac {\sin \alpha -\sin \beta }{\sin \alpha +\sin \beta }}.} Using the trigonometric identity, the factor formula for sines specifically sin ⁡ α ± sin ⁡...

(Yuanyong Luo et al.), is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions...

from a place to the Kaaba, and allows the exact calculation (hisab) of the qibla using a spherical trigonometric formula that takes the coordinates of a...

exact match on all constraints, and perhaps an even lower degree, if an approximate fit is acceptable. Other types of curves, such as trigonometric functions...

series, calculus, trigonometry, geometry, and algebra. He was the first to use infinite series approximations for a range of trigonometric functions, which...

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

parallax angle is 0.5 arcseconds, the object is 2 pc away; etc.). No trigonometric functions are required in this relationship because the very small angles...

The external secant function (exsecant, symbolized exsec) is a trigonometric function defined in terms of the secant function: exsec ⁡ θ = sec ⁡ θ − 1...

others. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar...