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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