Custom «Trigonometric Delights» Essay Paper Sample

Trigonometric Delights

Mathematics is a subject that is fundamental for achieving a better view on happenings that take place in our surrounding. It enhances decisive thinking and analytical abilities. One particular topic of mathematics that is of great importance is trigonometry. The word trigonometry itselfis derived from two Greek words "trigon" which refers to triangle, and "metria" whose English equivalent is measure. The two components of the word points to the initial conception that trigonometry would only be useful in determining sides and angles of a triangles. However, trigonometry is today understood as a field of mathematics that deals with triangles, circles, oscillations and waves.

Since its innovation, trigonometry has not only been limited to the mathematics discipline. It has been applicable in many fields such as surveying, physics and engineering. Trigonometry is thus very essential in countless other fields. It has been generally identified as a mathematical tool with many applications even in the present world. Ancient societies used right triangle trigonometry for the purpose of measuring angles and distances in surveying and astronomy, among other fields.

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Trigonometry has a varied history. Some of the initial applications of trigonometric functions like sine, cosine and tangents were associated with the chords of a circle. Hipparchus, the renowned Greek astronomer and mathematician created the first known table of chords in 140 BC. Fellow astronomers, Menelaus (ca. AD 100) and Ptolemy (ca. AD 100) further built upon his work by relying Babylonian customs. Babylonian and Greek influences fused with great mathematical advancements in India around AD 500 to generate a trigonometry closer to its contemporary form. Some of the Hindu mathematicians gave tables of half chords, which have connection to our modern concept of sine.

The investigation of the lengths of shadows of objects of an assortment of elevations led to the development of another set of trigonometric functions namely tangent and cotangent. In Egypt, Thales of Miletus made use of the length of shadows to work out the altitudes of the pyramids in around 600 BC. Other trigonometric functions such as secant and cosecant originated from tables initially used by navigators in the fifteenth century. The basis of trigonometric tradition in Indian and Arabic mathematics is derived from shadow lengths. This simple tradition has in turn influenced modern day trigonometry.

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Once mathematicians came up with broader definitions for sine, cosine and tangent, trigonometry turned out to be equally important in mathematics and science. The general descriptions for the trigonometric functions were developed by regarding these values as points on a unit circle. Although many centuries have passed since its origin, trigonometry is being applied in many areas. Graphs of sine, cosine and tangent functions are periodic. Mathematicians and scientists use trigonometric functions to explain a variety of natural phenomena which take place periodically. For instance, trigonometric functions are used to determine the time when the sun sets or rises. Furthermore, they can be used to describe the seasonal changes in temperature.

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Trigonometry is not limited to the description of phenomena. It is also useful in developing computer music since sound travels in waves though the pattern which is not as regular as a sine or cosine functions. Trigonometry finds an ideal application in modern architecture. The magnificently curved surfaces made of metal, stone and glass would be unachievable if not for the great potential of this branch of mathematics.

In conclusion, the discipline which started as a simple measurement of the angles and sides of triangles is today one of the pillars of mathematics. Its application in other fields such as sciences remains very significant.

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