154427867 Ppt on Trigonometry Class 10

8/18/2019 154427867 Ppt on Trigonometry Class 10

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Applications ofTrigonometry Name-Yatharth Singh

Class- X th

Roll No.-41School-K.V. -5, Mansarovar,Jaipur


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History of Trigonometry

• The 'abylonian astronomers ()*++ 'Ckept detailed records on the rising andsetting of stars, the motion of theplanets, and the solar and lunar

eclipses, all of which required familiaritywith angular distances measured on thecelestial sphere. "ome have evenasserted that the ancient 'abylonianshad a table of secants.

• The -gyptians used a primitive form oftrigonometry for building pyramids inthe nd millennium 'C.


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• The next significant developments of trigonometrywere in /ndia. /nfluential works from the 0th12thcentury, known as the "iddhantas first defined the

sine as the modern relationship between half anangle and half a chord, while also defining thecosine, versine, and inverse sine.

• "oon afterwards, another /ndian mathematician andastronomer, 3ryabhata , collected and expandedupon the developments in his work, 3ryabhatiya.

• The "iddhantas and the 3ryabhatiya contain theearliest surviving tables of sine values and versine ()4 cosine values.


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Trigonometry Formulae & their Full

forms……..Sin(sine)- perpendicular/hypotenuse

Cos(cosine)-base/hypotenuse

Tan(tangent)- perpendicular/base

Cosec(cosecant)-hypotenuse/perpendicular

Sec(secant)-hypotenuse/base

Cot(cotangent)-base/perpendicular


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3pplications of Trigonometry3pplications of Trigonometry

• There is an enormous number of applications of trigonometry andtrigonometric functions. For instance, the technique of triangulation isused in astronomy to measure the distance to nearby stars, ingeography to measure distances between landmarks, and in satellite

navigation systems. The sine and cosine functions are fundamental tothe theory of periodic functions such as those that describe sound andlight waves.

• /n the following slides, we will learn what is line of sight, angle ofelevation, angle of depression, and also solve some problems relatedto trigonometry using trigonometric ratios.


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Line of Sight

"uppose a boy is looking at a bird on a tree, so theline 5oining the eye of the boy and the bird is calledthe Line of "ight.

L i n e o f "

i g h t


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Angle of Elevation

Lets take the same case again that a boy is looking ata bird on a tree. The angle which the line of sightmakes with a hori6ontal line drawn away from theeyes is called the angle of elevation.

3ngle of -levation


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Angle of Depression

7ow if we consider that the bird is looking at the boy,

then the angle between the bird8s line of sight andhori6ontal line drawn from its eyes is called the 3ngleof 9epression.

3ngle of 9epression


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Lets now solve some

examples…O Following are some very simple examples of the

application of trigonometry.

O /n the first example, you have to find the distance ofa man from the building as well as the distancebetween him and the top of the tower.

O /n the second example, you have to find


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Examples…O 3 man is standing at a distance from a building of height :+ m. The

angle of elevation from the man8s eyes to the top of the tower is 02degrees. Find the distance of the man from the building as well as the

distance between him and the top of the tower.

C(man)

A

45˚

!"m


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O 9istance ('C

tan02; < ) < 3'='C < :+='C 'C < :+ m

Therefore, the distance between the man and the tower is :+meters.

O 7ow, Finding 3C sin02; < )=> < :+=3C

3C < :+ > meters

Thus, the distance between the man and the top of the tower is :+> meters.


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154427867 Ppt on Trigonometry Class 10

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