Post on 04-Apr-2018
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Trigonometry- derived from
the words trigonon which
means triangle and
metron which means to
measure. A branch of mathematics
concerned with the
relationship between angles
and their sides and the
calculations based on them.
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Trigonometry was first
invented by the Greeks,
and was used for
navigation and astronomy.
It was first used by Hipparchus
in 150 BC. He started out withcreating 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.
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During Medieval times,
the Chinese developed the tangent
function, and the Indians created sine
and cosine tables. They also helped todevelop the formal definitions for
cosine, cotangent, secant, and
cosecant.
In 1559, Bartholemaeus
Pitiscus published a workcalled Trigonometry, which
is probably where we get the
name today.
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Pitiscus
Hipparchus
Aryabhata
Regiomonatus
Guo Shoujing
Theodosius
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Although Pitiscus worked much in the
theological field, his proper abilities concerned
mathematics, and particularly trigonometry.
The word 'trigonometry' is due to Pitiscus and first
occurs in the title of his work Trigonometria: sive desolutione triangulorum tractatus brevis et
perspicuus first published in Heidelberg in 1595 as
the final section of A Scultetus's Sphaericorum libri
tres methodice conscripti et utilibus scholiis expositi.
The first section, divided into five books, coversplane and spherical trigonometry.
In the first book he introduced the main definitions
and theorems of plane and spherical trigonometry.
The third of the five books is devoted to plane
trigonometry and it consists of six fundamentaltheorems.
The fourth book consists of four fundamental
theorems on spherical trigonometry, while the fifth
book proves a number of propositions on the
trigonometric functions.
Trigonometry: or, the doctrine of triangles.
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He made an early contribution to
trigonometry producing a table of chords,
an early example of a trigonometric
table; indeed some historians go so far as
to say that trigonometry was invented byhim.
Finally let us examine the contributions
which Hipparchus made to
trigonometry.
Even if he did not invent it, Hipparchus is
the first person whose systematic use of
trigonometry we have documentary
evidence.
If this is so, Hipparchus was not only the
founder of trigonometry but also the
man who transformed Greek astronomy
from a purely theoretical into a practical
predictive science.
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The mathematical part of the
Aryabhatiya covers arithmetic,
algebra, plane trigonometry
and spherical trigonometry.
We now look at the
trigonometry contained in
Aryabhata's treatise.
He also introduced the versine(versin = 1 - cosine) into
trigonometry.
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Regiomontanus made important
contributions to trigonometry and
astronomy.
In the Epitome Regiomontanus, realising
the need for a systematic account of
trigonometry to support astronomy,
promised to write such a treatise.
With Book II the study of trigonometry
gets under way in earnest.
Books III, IV and V treat spherical
trigonometry which, of course, is of major
importance in astronomy.
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Making sense of the data gathered from the
instruments required a knowledge of
spherical trigonometry and Guo devised
some remarkable formulae.
We should now look at the rather remarkable
work which Guo did on sphericaltrigonometry and solving equations.
The first column is the value of x using Guo's
formula taking an accurate modern
approximation to , the second column is the
result given by the formula with = 3, while
the third column is the correct answer
calculated using trigonometry (in fact the
cosine).
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Sphaerics contains no trigonometry
although it is likely that Hipparchusintroduced spherical trigonometry
before Sphaerics was written
(although, one has to assume, after
the book on which Sphaerics is based,which would certainly be the case if
this earlier book was written by
Eudoxus).
Perhaps it is worth remarking that
despite our comment above that the
work contains no trigonometry, there
are some results which we could easily
interpret in trigonometrical terms.
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Astronomy has been studied formillennia by civilizations in all
regions of the world. In our modern age, being able
to apply Astronomy helps us tocalculate distances betweenstars and learn more about the
universe. Astronomers use the method of
parallax, or the movement ofthe star against the backgroundas we orbit the Sun, to discover
new information about galaxies. Menelaus Theorem helps
astronomers gather informationby providing a back drop inspherical triangle calculation.
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Trigonometry is used in geology to
estimate the true dip of beddingangles. Calculating the true dip
allows geologists to determine the
slope stability.
Although not often regarded asan integral profession, geologists
contribute to the safety of many
building foundations.
Any adverse bedding conditionscan result in slope failure and the
entire collapse of a structure.
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http://ph.answers.yahoo.com/question/index?qid=
20080617061145AA7Gk8E
http://www.hackingtheuniverse.com/science/histo
ry-of-science-and-
technology/genarticles/timeline-of-trigonometry
http://www.clarku.edu/~djoyce/trig/apps.html
http://www.edurite.com/kbase/examples-of-
trigonometry-in-nature
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