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7/26/2019 Tirg Presentation

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NAMES

MMADINARE SENIOR SCHOOL



APPLICATIONS OF

TRIGONOMETRY



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&



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&.



• 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.



• 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.



• 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.



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



Astrono!y

• For instance, the technique

of triangulation is used in

astronomy to measure the

distance to nearby stars.



Ar$'ite$t%re



Medi$ine



Geora"'y

• in geography to measure

distances between

landmarks



Me$'ani$a# enineerin



P'ysi$s

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