This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations.(December 2018) (Learn how and when to remove this message)
Trigonometry
Outline
History
Usage
Functions (sin, cos, tan, inverse)
Generalized trigonometry
Reference
Identities
Exact constants
Tables
Unit circle
Laws and theorems
Sines
Cosines
Tangents
Cotangents
Pythagorean theorem
Calculus
Trigonometric substitution
Integrals (inverse functions)
Derivatives
Trigonometric series
Mathematicians
Hipparchus
Ptolemy
Brahmagupta
al-Hasib
al-Battani
Regiomontanus
Viète
de Moivre
Euler
Fourier
v
t
e
In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering. The calculation of mathematical tables was an important area of study, which led to the development of the first mechanical computing devices.
Modern computers and pocket calculators now generate trigonometric function values on demand, using special libraries of mathematical code. Often, these libraries use pre-calculated tables internally, and compute the required value by using an appropriate interpolation method. Interpolation of simple look-up tables of trigonometric functions is still used in computer graphics, where only modest accuracy may be required and speed is often paramount.
Another important application of trigonometric tables and generation schemes is for fast Fourier transform (FFT) algorithms, where the same trigonometric function values (called twiddle factors) must be evaluated many times in a given transform, especially in the common case where many transforms of the same size are computed. In this case, calling generic library routines every time is unacceptably slow. One option is to call the library routines once, to build up a table of those trigonometric values that will be needed, but this requires significant memory to store the table. The other possibility, since a regular sequence of values is required, is to use a recurrence formula to compute the trigonometric values on the fly. Significant research has been devoted to finding accurate, stable recurrence schemes in order to preserve the accuracy of the FFT (which is very sensitive to trigonometric errors).
A trigonometry table is essentially a reference chart that presents the values of sine, cosine, tangent, and other trigonometric functions for various angles. These angles are usually arranged across the top row of the table, while the different trigonometric functions are labeled in the first column on the left. To locate the value of a specific trigonometric function at a certain angle, you would find the row for the function and follow it across to the column under the desired angle.[1]
^"Trigonometry Table: Learning of trigonometry table is simplified". Yogiraj notes | General study and Law study Notes. Retrieved 2023-11-02.
and 28 Related for: Trigonometric tables information
mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometrictables were essential...
trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions...
earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied...
Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic...
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometrictables were used in ancient Greece...
/ 4 ) = 2 / 2 {\displaystyle \cos(\pi /4)={\sqrt {2}}/2} . While trigonometrictables contain many approximate values, the exact values for certain angles...
indicates how many times one number contains another TrigonometryTrigonometric functions Trigonometric identities Euler's formula Archimedes Aristarchus...
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...
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:...
versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Aryabhatia, Section I) trigonometrictables. The versine of an angle...
are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation...
(antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals...
medical practitioner, and teacher. He is perhaps best known for his trigonometrictables and as Nicolaus Copernicus's sole pupil. He facilitated the publication...
There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen...
and where he collated Greek manuscripts for a handsome salary. The trigonometrictables that he created while living in Hungary, his Tabulae directionum...
others. He developed trigonometry and constructed trigonometrictables, and he solved several problems of spherical trigonometry. With his solar and lunar...
using a different trigonometric form. To illustrate, let us assume we had available seven-place logarithm and trigonometrictables, and wished to solve...
Along with the trigonometrictables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (zijes). In particular...
In mathematics, a trigonometric substitution replaces a trigonometric function for another expression. In calculus, trigonometric substitutions are a...
addition, and logarithmic versions of trigonometrictables further saved labor by reducing the number of necessary table lookups. The external secant or external...
pages of tables of trigonometric functions and their natural logarithms. These tables greatly simplified calculations in spherical trigonometry, which are...
of trigonometric functions of angles related to 2 π / 7 {\displaystyle 2\pi /7} satisfy cubic equations. Given the cosine (or other trigonometric function)...
convenient enough that tables of haversine values and logarithms were included in 19th- and early 20th-century navigation and trigonometric texts. These days...
The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change...
in math and physics Generating primes Generating set Generating trigonometrictables Other: Generated collection, in music theory Generate LA-NY, digital...
In mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions...
logarithms that would supplant it. The trigonometric identities exploited by prosthaphaeresis relate products of trigonometric functions to sums. They include...
Global Information
