Beginnings of Trigonometry
Trigonometry is an area of mathematics used for determining geometric quantities. Its name, first published in 1595 by B. Pitiscus, means "the study of trigons (triangles)" in Latin. Ancient Greek Mathematicians first used trigonometric functions with the chords of a circle. The first to publish these chords in 140 BC was Hipparchus, who is now called the founder of trigonometry. In AD 100, Menelaus, another Greek mathematician, published six lost books of tables of chords. Ptolemy, a Babylonian, also wrote a book of chords. Using chords, Ptolemy knew that
sin (x + y) = sin x * cos y + cos x * sin y
and
a / sin A = b / sin B = c / sin C.
Sine first appeared in the work of Aryabhata, a Hindu. He used the word jya for sine. He also published the first sine tables. Brahmagupta, in 628, also published a table of sines for any angle. Jya became jiba in translation and jiba became jaib in later writings. Jaib means fold in Arabic. This was translated into sinus, or fold in Latin. In 1533, Regiomontanus’ published De triangulis omnimodis which dealt with planar trigonometry and inverses. Later, Rheticus published Copernicus’ book dealing with Trigonometry in Astronomy in 1542. Edmund Gunter first used the abbreviation sin in 1624. Sin was first used in a book in 1634. Other variances still were popular. Other variances for cosine and tangent were also still very popular, especially among different languages. Although sine, cosine, and tangent were used very much by astronomers and surveyors, the functions secant and cosecant were of little use to these practical minded mathematicians.
Trigonometry has been used throughout modern and ancient history dealing with practical applications, such as surveying. Modernly, it has incorporated many other ideas instead of just triangles. The six trigonometric functions now known are
sine (sin) = opposite side/ hypotenuse
cosine (cos) = adjacent side/ hypotenuse
tangent (tan) = opposite side/ adjacent
secant (sec) = hypotenuse/ adjacent side
cosecant (cosec) = hypotenuse/ opposite side
cotangent (cot) = adjacent side/ opposite side
Three of these ratios are the reverse of other ratios. All of these ratios are used widely to determine sides and angles of triangles. Without their discovery, surveyors and other practical mathematicians would not be able to efficiently determine relationships.