tirg presentation
TRANSCRIPT
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NAMES
MMADINARE SENIOR SCHOOL
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APPLICATIONS OF
TRIGONOMETRY
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PURPOSE OF STUDY
• Defnition and History o Triono!etry
• A""#i$ations o Triono!etry in rea# #iesit%ations&
• C%rrent C'a##enes t'at $an (e so#)ed(y triono!etry&
• Co!!on "ro(#e!s t'at !ay arise *'en
triono!etry is not a""#ied&• Re$o!!endations on t'e a""#i$ations o
triono!etry&
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Introd%$tion + What is Trigonometry?
• Trigonometry is a methodology for finding some unknown elements
of a triangle provided the data includes a sufficient amount of linear
and angular measurements to define a shape uniquely.
• For example, two sides a and b of a triangle and the angle they
include define the triangle uniquely. The third side c can then be
found from the Law of Cosines while the angles and ! are
determined from the Law of "ines.
• Trigonometry is derived from #reek words trig$non, meaning
%triangle% and metron, meaning %measure&.
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• The 'abylonian astronomers ()*++
'C kept detailed records on the rising
and setting of stars, the motion of the
planets, and the solar and lunar
eclipses, all of which required
familiarity with angular distances
measured on the celestial sphere.
"ome have even asserted that the
ancient 'abylonians had a table of
secants.
• The -gyptians used a primitive form of
trigonometry for building pyramids in
the nd millennium 'C.
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• The next significant developments of
trigonometry were in /ndia. /nfluential works
from the 0th12th century, known as the
"iddhantas first defined the sine as the
modern relationship between half an angle
and half a chord, while also defining thecosine, versine, and inverse sine.
• "oon afterwards, another /ndian
mathematician and astronomer, 3ryabhata ,
collected and expanded upon the
developments in his work, 3ryabhatiya.
• The "iddhantas and the 3ryabhatiya contain
the earliest surviving tables of sine values
and versine () 4 cosine values.
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• The next significant developments of trigonometry
were in /ndia. /nfluential works from the 0th12th
century, known as the "iddhantas first defined
the sine as the modern relationship between half
an angle and half a chord, while also defining the
cosine, versine, and inverse sine.
• "oon afterwards, another /ndian mathematicianand astronomer, 3ryabhata , collected and
expanded upon the developments in his work,
3ryabhatiya.
• The "iddhantas and the 3ryabhatiya contain the
earliest surviving tables of sine values and
versine () 4 cosine values.
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3pplications of Trigonometry
• Line o si't
• Ar$'ite$t%re
• E#e$troni$s
• Land s%r)eyin
• Me$'ani$a#Enineerin
• Ci)i# enineerin• O"ti$s
• P'ysi$a# s$ien$es
• O$eanora"'y• Seis!o#oy
• P'ar!a$o#oy
• A)iation• P'ar!a$o#oy
• Pro(a(i#ity t'eory
• Statisti$s• E#e$tri$a#
Enineerin
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Astrono!y
• For instance, the technique
of triangulation is used in
astronomy to measure the
distance to nearby stars.
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Ar$'ite$t%re
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Medi$ine
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Geora"'y
• in geography to measure
distances between
landmarks
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Me$'ani$a# enineerin
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P'ysi$s