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The term "trigonometry" was derived from Greek τρίγωνον trigōnon, "triangle" and μέτρον metron, "measure". [3]The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic (see Sine and cosine § Etymology).
Trigonometry has been noted for its many identities, that is, equations that are true for all possible inputs. [83] Identities involving only angles are known as trigonometric identities. Other equations, known as triangle identities, [84] relate both the sides and angles of a given triangle.
4th to 5th centuries: The modern fundamental trigonometric functions, sine and cosine, are described in the Siddhantas of India. [75] This formulation of trigonometry is an improvement over the earlier Greek functions, in that it lends itself more seamlessly to polar co-ordinates and the later complex interpretation of the trigonometric functions.
James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer.His surname is sometimes spelt as Gregorie, the original Scottish spelling.He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.
They are significant in that they contain the first instance of trigonometric relations based on the half-chord, as is the case in modern trigonometry, rather than the full chord, as was the case in Ptolemaic trigonometry. [137] Through a series of translation errors, the words "sine" and "cosine" derive from the Sanskrit "jiya" and "kojiya". [137]
260 BC – Greece, Archimedes proved that the value of π lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base ...
A chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120 parts. Ptolemy used a circle whose diameter is 120 parts. He tabulated the length of a chord whose endpoints are separated by an arc of n degrees, for n ranging from 1 / 2 to 180 by increments of 1 / 2 .
These are claimed to first appear in his 1608 edition of Trigonometria in the added trigonometric tables [5] and can also be found in the 1612 edition. [6] However, others argue that the use of the '.' symbol only constitute a way of grouping numbers and that the mixed use of decimal points and fractions as well as multiple decimal points do ...