It was first used by Hipparchus in 150 BC. He started out with creating a bunch of tablets with certain ratios. He then went on to start to define chord, sine, and cosine. Claudius Ptolemy continued Hipparchus’ work, and improved on his tables. He was also able to figure out how to calculate square roots. He then continued to work on Sine and Cosine rules, and defined for us the inverse functions of Sine and Cosine. Also during the 10th and 11th centuries in Egypt, mathematicians were able to determine other formulas.

During Medieval times, the Chinese developed the tangent function, and the Indians created sine and cosine tables. They also helped to develop the formal definitions for cosine, cotangent, secant, and cosecant.

In 1559, Bartholemaeus Pitiscus published a work called “Trigonometry”, which is probably where we get the name today.

Until the 17th century, all of the functions that are known today were calculated by given tables, but during this time, equations began to be put together, to allow calculating the sine and cosine with tables

In the 17th century, John Napier helped to develop the log functions and developed some equations to solve oblique triangles.

Sources:

http://en.wikipedia.org/wiki/Trigonometry

http://library.thinkquest.org/C0110248/trigonometry/history1.htm

http://www.cartage.org.lb/en/themes/sciences/Mathematics/Trigonometry/history/History%20.html

http://web.math.unifi.it/archimede/archimede_NEW_inglese/trigonometria/trigonometria/trigo5.html