HISTORY OF TRIGONOMETRY
The history of trigonometry goes back to the earliest recorded mathematics in Egypt and Babylon. The Babylonians established the measurement of angles in degrees, minutes, and seconds. Not until the time of the Greeks, however, did any considerable amount of trigonometry exist. In the 2nd century bc the astronomer Hipparchus compiled a trigonometric table for solving triangles. Starting with 7½° and going up to 180° by steps of 7½°, the table gave for each angle the length of the chord subtending that angle in a circle of a fixed radius r. Such a table is equivalent to a sine table. The value that Hipparchus used for r is not certain, but 300 years later the astronomer Ptolemy used r = 60 because the Hellenistic Greeks had adopted the Babylonian base-60 (sexagesimal) numeration system.
In his great astronomical handbook, The Almagest, Ptolemy provided a table of chords for steps of y°, from 0° to 180°,that is accurate to 1/3600 of a unit. He explained his method for constructing his table of chords, and in the course of the book he gave many examples of how to use the table to find unknown parts of triangles from known parts.
Indian astronomers had developed a trigonometric system based on the sine function rather than the chord function of the Greeks. This sine function, unlike the modern one, was not a ratio but simply the length of the side opposite the angle in a right triangle of fixed hypotenuse. The Indians used various values for the hypotenuse.
Late in the 8th century, Muslim astronomers inherited both the Greek and the Indian traditions, but they seem to have preferred the sine function. Trigonometric calculations were greatly aided by the Scottish mathematician John Napier.
Finally, in the 18th century the Swiss mathematician Leonhard Euler defined the trigonometric functions in terms of complex numbers. This made the whole subject of trigonometry just one of the many applications of complex numbers, and showed that the basic laws of trigonometry were simply consequences of the arithmetic of these numbers.