{\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...

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...

In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle:...

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...

during the 2nd millennium BC. 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...

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

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

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

For small angles, the trigonometric functions sine, cosine, and tangent can be calculated with reasonable accuracy by the following simple approximations:...

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...

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

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

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...

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

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

set of values of the trigonometric sine function in a conventional sense; it is a table of the first differences of the values of trigonometric sines expressed...

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

the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and...

formats). In the table above, integer values are exact, whereas values in decimal notation (e.g. 1.0) are rounded values. The minimum exponents listed are...

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...

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...

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

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 ⁡...

and the technique gives two possible values for the enclosed angle. The law of sines is one of two trigonometric equations commonly applied to find lengths...

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