TRIGONOMETRY -The complex origins of trigonometry are embedded in the history of the simple word "sine," a mistranslation of an Arabic transliteration of a Sanskrit mathematical term! The complex etymology of "sine" reveals trigonometry's roots in Egyptian, Babylonian, Greek, Hellenistic, Indian, and Arabic mathematics and astronomy. The earliest uses of trigonometric functions were related to the chords of a circle, and the recognition that the length of the chord subtended by a given angle x was (in modern terms) 2sin(x/2). The Greek astronomer and mathematician Hipparchus produced the first known table of chords in 140 BC. His work was further developed by astronomers Menelaus (ca. AD 100) and Ptolemy (ca. AD 100), who relied on Babylonian observations and traditions
Babylonian and Greek influences mingled with rich native mathematical
developments in India around AD 500 to produce a trigonometry closer to its modern form.
Hindu mathematical works such as that of Aryabhata give tables of half chords, known by
the term jya-ardha or simply jya, which bears the following relationship to our modern
concept of sine: jya x = r sinx.From India the sine function was introduced to the Arab
world in the 8th century, where the term jya was transliterated into jiba or jyb.
Early Latin translations of Arabic mathematical treatises mistook jiba for the Arabic
word jaib, which can mean the opening of a woman's garment at the neck. Accordingly,
jaib was translated into the Latin sinus, which can mean "fold" (in a garment), "bosom,
" "bay," or even "curve." Hence our word "sine."
Another set of trigonometric functions, tangent and cotangent, developed
from the study of the lengths of shadows cast by objects of various heights. Thales
of Miletus used shadow lenghts to calculate the heights of the pyramids in around 600 BC,
just as the Egyptians had done several millenium earlier. Both Indian and Arabic mathematics
developed a trigonometric tradition based on shadow lengths, a tradition that, in turn, influenced
European mathematics.
As for the word "trigonometry," it first appeared as the title of a book Trigonometria
(literally, the measuring of triangles), published by Bartholomeo Pitiscus in 1595.
trigonometry - 1614, from Mod.L. trigonometria, from Gk. trigonon "triangle"
(from tri- "three" + gonia "angle") + metron "a measure."
Prequisite:College Algebra
Today, trigonometry is introduced to students as a method for finding the
missing parts of right triangles. In this form it is used by surveyors,
architects and engineers, as well as navigators and astronomers. So, it
is pretty important.
The second level of trigonometry for today's students is circular trig.
Students learn to see the sine, cosine and tangent ratios as they change
as the size of the reference angles changes. This graphs out as a wave
shaped curve (sine wave) and can be used to represent sound, light, radio
and many other wave forms, so scientist and engineers have found
extensive uses for circular trig.
Trig is an essential tool of The Calculus, so all students who intend to
study mathematics at higher levels must include trig in their basic learning.