Shivansh Trigo

7/31/2019 Shivansh Trigo

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Shivansh Gaba

X-C

Roll No: 34


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WHAT ISTRIGONOMETRY?Trigonometry in basic words is the mathematics of triangles and

trigonometric functions.

The word Trigonometry comes from the Greek words: Trigononmeaning triangle and metron meaning a measure.

In a broader sense, trigonometry is that branch if mathematicswhich deals with the measurement of the sides and the angles of atriangle and the problems allied with angles.


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SINE

The first use of the idea of sinein the way we use it today was in

the workAryabhatiyam byAryabhata in A.D. 500.

Aryabhata used the word

ardha-jya for the half chordwhich came to be known as

jiva in due course.Later, jiva came to be known

as sinusand later as sine.An English Professor Edmund

Gunter (1581-1626) first used the

abbreviated notation sin .

Trigonometry is not the work of any one person or nation. Its history spans

thousands of years and has touched every major civilization.

AryabhataA.D. 476-550


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The origin of the termscosine and tangentwas much later. The cosinefunction arose from the needto compute the sine of the

complementary angle.

Aryabhata called kotijya.

The name cosinus

originated with EdmundGunter. In 1674, the EnglishMathematician Sir JonasMoore first used the

abbreviated notation cos

COSINE AND TANGENT


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RATIOS

TangentTangent tantan OppositeOppositeAdjacentAdjacent

CotangentCotangent cotcot AdjacentAdjacentOppositeOpposite

SecantSecant secsec HypotenuseHypotenuseAdjacentAdjacent

CosecantCosecant coseccosec HypotenuseHypotenuse

OppositeOpposite

SineSine sinsin OppositeOppositeHypotenuseHypotenuse

CosineCosine coscos AdjacentAdjacentHypotenuseHypotenuse

Note: The formulas provided

are in respect to the picture.

The Cosecant, Secant, and CotangentThe Cosecant, Secant, and Cotangentare the Reciprocals ofare the Reciprocals ofthe Sine, Cosine,and Tangent respectively .the Sine, Cosine,and Tangent respectively .


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THE TRIGONOMETRICVALUES

Angle AAngle A 00o

3030o

4545o

6060o

9090o

sin Asin A 00 11

22

11

22

33

22

11

cos Acos A 11 33

22

11

22

11

22

00

tan Atan A 00 11

33

11 33 NotNotDefinedDefined

cosec Acosec A NotNotDefinedDefined

22 22 22

33

11

sec Asec A 11 22

33

22 22 NotNotDefinedDefined

cot Acot A NotNotDefinedDefined

33 11 11

33

00


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Basic TrigonometricIdentities

)cos()sin()tan(

A

AA =

)sin()cos()cot(

A

AA =

)csc(1)sin(

)sin(

1)csc(

AA

AA

=

=

)sec(

1)cos(

)cos(

1)sec(

AA

AA

=

=

)cot(

1)tan(

)tan(

1)cot(

AA

AA

=

=

1)(cos)(sin11

=+ AA

)(sec1)(tan 11 AA =+

)(cos)(cot111AecA =+

Quotient identities:

Reciprocal Identities:

Pythagorean Identities:


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HOW TO USE TRIGONOMETRY INREAL LIFE?

Objective : To find the angle of elevation of a room .

Knowledge Required : 1. Trigonometric Ratios2. Trigonometric Values (acute

angles)

Materials Required : 1. A meter stick

2. A measuring tape

The project given is elaborated as follows:


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PERFORMING THE TASK !!Take the meter stick and put it horizontally on the wall to

measure the length .

Now, with the help of an adult measure the diagonal distance(hypotenuse) of your room.

Record the length in centimeters and convert it into meters.

Take the ratio of the length of the stick to the diagonaldistance to your room.

Use the trigonometric ratios to find out the angle of elevationof your room !!

THE MUCH AWAITED


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THE MUCH AWAITEDRESULT I performed the activity mentioned and since I took the ratio

of wall to the diagonal my ratio was as follows :

Perpendicular (opposite)

Hypotenuse

We already know that this value is equal to sin.

Now the values I got were:

Perpendicular = 6 mts.

Hypotenuse = 12mts.


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THERES THE ANSWER!!!

Sin A = Perpendicular

Hypotenuse

= 6 (Putting the

Values)12

Sin A = 1

2

Sin A = Sin 30o Angle of Elevation = 30

o


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THANK YOUTHANK YOU

Shivansh Trigo

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