. "En trigonometrisk tabell \u00E4r en tabell med v\u00E4rden f\u00F6r trigonometriska funktioner. S\u00E5dana tabeller var viktiga innan funktionsr\u00E4knedosor b\u00F6rjade tillverkas."@sv . . . . . "Les tables de fonctions trigonom\u00E9triques sont utiles dans beaucoup de domaines. Avant l'existence des calculatrices de poche, les tables trigonom\u00E9triques \u00E9taient essentielles pour la navigation, dans les sciences et dans la technologie.La r\u00E9alisation de tables de valeurs approch\u00E9es des fonctions repr\u00E9sentait un domaine d'\u00E9tude important, et mena au d\u00E9veloppement des premiers dispositifs de calcul m\u00E9caniques. Les ordinateurs modernes et les calculatrices de poche g\u00E9n\u00E8rent maintenant les valeurs des fonctions trigonom\u00E9triques \u00E0 la demande, en utilisant des biblioth\u00E8ques de code math\u00E9matique. Souvent, ces biblioth\u00E8ques utilisent des tables internes calcul\u00E9es d'avance, et la valeur requise est obtenue en utilisant une m\u00E9thode d'interpolation appropri\u00E9e. Des tables trigonom\u00E9triques simples sont maintenant souvent utilis\u00E9es en infographie, o\u00F9 en g\u00E9n\u00E9ral des valeurs pr\u00E9cises ne sont pas n\u00E9cessaires et les calculs doivent \u00EAtre effectu\u00E9s tr\u00E8s rapidement."@fr . . "150170"^^ . . . . . . . . . . . . . "Trigonometrisk tabell"@sv . . . . "En matem\u00E1ticas, las tablas de funciones trigonom\u00E9tricas son \u00FAtiles en varias \u00E1reas. Antes de la existencia de las calculadoras de bolsillo, las tablas trigonom\u00E9tricas eran esenciales para la navegaci\u00F3n, la ciencia y la ingenier\u00EDa.\u200B El c\u00E1lculo de las tablas matem\u00E1ticas fue un \u00E1rea de estudio importante, que condujo al desarrollo de los primeros dispositivos de computaci\u00F3n mec\u00E1nica.\u200B En este art\u00EDculo se describen resumidamente las t\u00E9cnicas de programaci\u00F3n y los algoritmos inform\u00E1ticos que permiten calcular los valores de funciones trigonom\u00E9tricas de gran precisi\u00F3n que requieren algunos c\u00E1lculos matem\u00E1ticos. Para las tradicionales tablas impresas en papel, v\u00E9ase el art\u00EDculo Tabla matem\u00E1tica."@es . . . . . "Tavola trigonometrica"@it . . "\u062C\u062F\u0627\u0648\u0644 \u0645\u062B\u0644\u062B\u064A\u0629"@ar . . . "En matem\u00E1ticas, las tablas de funciones trigonom\u00E9tricas son \u00FAtiles en varias \u00E1reas. Antes de la existencia de las calculadoras de bolsillo, las tablas trigonom\u00E9tricas eran esenciales para la navegaci\u00F3n, la ciencia y la ingenier\u00EDa.\u200B El c\u00E1lculo de las tablas matem\u00E1ticas fue un \u00E1rea de estudio importante, que condujo al desarrollo de los primeros dispositivos de computaci\u00F3n mec\u00E1nica.\u200B"@es . . "En matem\u00E0tiques, les taules de valors de les funcions trigonom\u00E8triques s\u00F3n \u00FAtils en diverses \u00E0rees. Abans de l'exist\u00E8ncia de les calculadores les taules trigonom\u00E8triques eren essencials per a la navegaci\u00F3, la ci\u00E8ncia i l'enginyeria.Avui, els ordinadors moderns i les calculadores de butxaca, generen els valors de les funcions trigonom\u00E8triques fent servir llibreries especials de codi matem\u00E0tic. Sovint, aquestes llibreries fan servir internament taules precalculades, i llavors calculen els valors que es requereix fent servir els m\u00E8todes adequats d'interpolaci\u00F3. La interpolaci\u00F3 a partir de taules senzilles de funcions trigonom\u00E8triques es fa servir encara en , on els c\u00E0lculs precisos ni calen ni es poden fer prou r\u00E0pid. Una altra aplicaci\u00F3 important de les taules trigonom\u00E8triques \u00E9s en els algorismes de generaci\u00F3 de la Transformada R\u00E0pida de Fourier (FFT, en angl\u00E8s: \"Fast Fourier Tranforsm\"), on els mateixos valors de funcions trigonom\u00E8triques (anomenats factors de gir) han de ser avaluats molts cops per a una transformada donada, especialment en al cas habitual on s'han de calcular moltes transformades de la mateixa mida. En aquest cas, l'estrat\u00E8gia de cridar cada cop una rutina d'una llibreria gen\u00E8rica es fa inacceptablement lent. Una opci\u00F3 \u00E9s la de cridar les rutines de la llibreria nom\u00E9s un cop per a cada angle, i anar construint una taula amb els valors trigonom\u00E8trics que es necessitaran, aix\u00F2 necessita una quantitat significativa de mem\u00F2ria per a emmagatzemar la taula. Un altre possibilitat, donat que el que es necessita \u00E9s una successi\u00F3 de valors distribu\u00EFts uniformement, \u00E9s fer servir una f\u00F3rmula recurrent per a calcular el valors trigonom\u00E8trics \"al vol\". S'han dedicat significatius esfor\u00E7os de recerca per tal de trobar algorismes recurrents estables i precisos, per tal de preservar la precisi\u00F3 de la FFT (la qual \u00E9s molt sensible als errors trigonom\u00E8trics)."@ca . . . . . . "En trigonometrisk tabell \u00E4r en tabell med v\u00E4rden f\u00F6r trigonometriska funktioner. S\u00E5dana tabeller var viktiga innan funktionsr\u00E4knedosor b\u00F6rjade tillverkas."@sv . . . . . . . . . . . . . . . . . . . "Trigonometric tables"@en . . . . . "Construcci\u00F3 de les taules trigonom\u00E8triques"@ca . "Construction des tables trigonom\u00E9triques"@fr . . . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062C\u062F\u0627\u0648\u0644 \u0642\u064A\u0645 \u0627\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0645\u0641\u064A\u062F\u0629 \u0641\u064A \u0639\u062F\u0629 \u0645\u062C\u0627\u0644\u0627\u062A. \u0642\u0628\u0644 \u0648\u062C\u0648\u062F \u0627\u0644\u0622\u0644\u0627\u062A \u0627\u0644\u062D\u0627\u0633\u0628\u0629 \u0627\u0644\u062C\u064A\u0628\u064A\u0629\u060C \u0643\u0627\u0646\u062A \u0627\u0644\u062C\u062F\u0627\u0648\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0636\u0631\u0648\u0631\u064A\u0629 \u0644\u0644\u0645\u0644\u0627\u062D\u0629 \u0648\u0627\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0637\u0628\u064A\u0642\u064A\u0629. \u0643\u0627\u0646 \u062D\u0633\u0627\u0628 \u0627\u0644\u062C\u062F\u0627\u0648\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0623\u062D\u062F \u0627\u0644\u0645\u062C\u0627\u0644\u0627\u062A \u0627\u0644\u0645\u0647\u0645\u0629 \u0644\u0644\u062F\u0631\u0627\u0633\u0629\u060C \u0645\u0645\u0627 \u0623\u062F\u0649 \u0625\u0644\u0649 \u062A\u0637\u0648\u064A\u0631 \u0623\u0648\u0644 \u0623\u062C\u0647\u0632\u0629 \u0627\u0644\u062D\u0648\u0633\u0628\u0629 \u0627\u0644\u0645\u064A\u0643\u0627\u0646\u064A\u0643\u064A\u0629. \u0627\u0644\u062D\u0648\u0627\u0633\u064A\u0628 \u0627\u0644\u062D\u062F\u064A\u062B\u0629 \u0648\u0627\u0644\u0622\u0644\u0627\u062A \u0627\u0644\u062D\u0627\u0633\u0628\u0629 \u0627\u0644\u062C\u064A\u0628\u064A\u0629 \u062A\u0648\u0644\u062F \u0627\u0644\u0622\u0646 \u0642\u064A\u0645 \u062F\u0627\u0644\u0629 \u0645\u062B\u0644\u062B\u064A\u0629 \u0639\u0646\u062F \u0627\u0644\u0637\u0644\u0628\u060C \u0648\u0630\u0644\u0643 \u0628\u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0645\u0643\u062A\u0628\u0627\u062A \u062E\u0627\u0635\u0629 \u0644\u0644\u0631\u0645\u0632 \u0627\u0644\u0631\u064A\u0627\u0636\u064A. \u063A\u0627\u0644\u0628\u064B\u0627 \u0645\u0627 \u062A\u0633\u062A\u062E\u062F\u0645 \u0647\u0630\u0647 \u0627\u0644\u0645\u0643\u062A\u0628\u0627\u062A \u0627\u0644\u062C\u062F\u0627\u0648\u0644 \u0627\u0644\u0645\u062D\u0633\u0648\u0628\u0629 \u0645\u0633\u0628\u0642\u064B\u0627 \u062F\u0627\u062E\u0644\u064A\u064B\u0627\u060C \u0648\u062A\u062D\u0633\u0628 \u0627\u0644\u0642\u064A\u0645\u0629 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629 \u0628\u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0637\u0631\u064A\u0642\u0629 \u0627\u0644\u0627\u0633\u062A\u064A\u0641\u0627\u0621 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629. \u0644\u0627 \u064A\u0632\u0627\u0644 \u064A\u062A\u0645 \u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0627\u0633\u062A\u064A\u0641\u0627\u0621 \u0627\u0644\u062C\u062F\u0627\u0648\u0644 \u0627\u0644\u0628\u062D\u062B \u0627\u0644\u0628\u0633\u064A\u0637\u0629 \u0644\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0641\u064A \u0627\u0644\u0631\u0633\u0648\u0645\u0627\u062A \u0627\u0644\u062D\u0627\u0633\u0648\u0628\u064A\u0629\u060C \u062D\u064A\u062B \u0642\u062F \u062A\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u062D\u0627\u062C\u0629 \u0625\u0644\u0649 \u062F\u0642\u0629 \u0645\u062A\u0648\u0627\u0636\u0639\u0629 \u0641\u0642\u0637 \u0648\u063A\u0627\u0644\u0628\u064B\u0627 \u0645\u0627 \u062A\u0643\u0648\u0646 \u0627\u0644\u0633\u0631\u0639\u0629 \u0642\u0635\u0648\u0649."@ar . . . . . . . . . . . . . . "En matem\u00E0tiques, les taules de valors de les funcions trigonom\u00E8triques s\u00F3n \u00FAtils en diverses \u00E0rees. Abans de l'exist\u00E8ncia de les calculadores les taules trigonom\u00E8triques eren essencials per a la navegaci\u00F3, la ci\u00E8ncia i l'enginyeria.Avui, els ordinadors moderns i les calculadores de butxaca, generen els valors de les funcions trigonom\u00E8triques fent servir llibreries especials de codi matem\u00E0tic. Sovint, aquestes llibreries fan servir internament taules precalculades, i llavors calculen els valors que es requereix fent servir els m\u00E8todes adequats d'interpolaci\u00F3."@ca . . "In matematica la tavola trigonometrica \u00E8 una tabella che elenca il valore di una funzione trigonometrica per un certo numero di possibili valori angolari. Una tavola trigonometrica \u00E8 principalmente caratterizzata da due aspetti: \n* dettaglio: indica la differenza tra due angoli consecutivi di cui la tabella riporta i valori; maggiore \u00E8 il dettaglio, minore \u00E8 la differenza; \n* precisione: indica con quale approssimazione sono arrotondati i valori della funzione trigonometrica riportati nella tavola."@it . . . . . "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."@en . . . . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062C\u062F\u0627\u0648\u0644 \u0642\u064A\u0645 \u0627\u0644\u062F\u0648\u0627\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0645\u0641\u064A\u062F\u0629 \u0641\u064A \u0639\u062F\u0629 \u0645\u062C\u0627\u0644\u0627\u062A. \u0642\u0628\u0644 \u0648\u062C\u0648\u062F \u0627\u0644\u0622\u0644\u0627\u062A \u0627\u0644\u062D\u0627\u0633\u0628\u0629 \u0627\u0644\u062C\u064A\u0628\u064A\u0629\u060C \u0643\u0627\u0646\u062A \u0627\u0644\u062C\u062F\u0627\u0648\u0644 \u0627\u0644\u0645\u062B\u0644\u062B\u064A\u0629 \u0636\u0631\u0648\u0631\u064A\u0629 \u0644\u0644\u0645\u0644\u0627\u062D\u0629 \u0648\u0627\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0637\u0628\u064A\u0642\u064A\u0629. \u0643\u0627\u0646 \u062D\u0633\u0627\u0628 \u0627\u0644\u062C\u062F\u0627\u0648\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0623\u062D\u062F \u0627\u0644\u0645\u062C\u0627\u0644\u0627\u062A \u0627\u0644\u0645\u0647\u0645\u0629 \u0644\u0644\u062F\u0631\u0627\u0633\u0629\u060C \u0645\u0645\u0627 \u0623\u062F\u0649 \u0625\u0644\u0649 \u062A\u0637\u0648\u064A\u0631 \u0623\u0648\u0644 \u0623\u062C\u0647\u0632\u0629 \u0627\u0644\u062D\u0648\u0633\u0628\u0629 \u0627\u0644\u0645\u064A\u0643\u0627\u0646\u064A\u0643\u064A\u0629."@ar . "11257"^^ . "1120902111"^^ . . "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)."@en . . . "In matematica la tavola trigonometrica \u00E8 una tabella che elenca il valore di una funzione trigonometrica per un certo numero di possibili valori angolari. Una tavola trigonometrica \u00E8 principalmente caratterizzata da due aspetti: \n* dettaglio: indica la differenza tra due angoli consecutivi di cui la tabella riporta i valori; maggiore \u00E8 il dettaglio, minore \u00E8 la differenza; \n* precisione: indica con quale approssimazione sono arrotondati i valori della funzione trigonometrica riportati nella tavola. Il dettaglio pu\u00F2 non essere costante per meglio mappare funzioni che abbiano asintoti verticali o orizzontali, che implicano significative variazioni del valore delle funzione in prossimit\u00E0 di alcuni valori angolari."@it . . . . . "Les tables de fonctions trigonom\u00E9triques sont utiles dans beaucoup de domaines. Avant l'existence des calculatrices de poche, les tables trigonom\u00E9triques \u00E9taient essentielles pour la navigation, dans les sciences et dans la technologie.La r\u00E9alisation de tables de valeurs approch\u00E9es des fonctions repr\u00E9sentait un domaine d'\u00E9tude important, et mena au d\u00E9veloppement des premiers dispositifs de calcul m\u00E9caniques."@fr . . . "Tablas trigonom\u00E9tricas"@es . . . .