TRIGONOMETRY INTRIGONOMETRY IN

SUPREIYA

CLASS : X - A

USE OFUSE OF

REAL LIFEREAL LIFE

WHAT IS TRIGONOMETRY?

Trigonometry in basic words is the mathematics of triangles and trigonometric functions.

The word “Trigonometry” comes from the Greek words: ‘Trigonon’ meaning ‘triangle’ and ‘metron’ meaning a ‘measure’.

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

ORIGIN OF ‘SINE’

The first use of the idea of ‘sine’ in the way we use it today was in the work Aryabhatiyam by Aryabhata in A.D. 500.

Aryabhata used the word ‘ardha-jya’ for the half chord which came to be known as ‘jiva’ in due course.

Later, ‘jiva’ came to be known as ‘sinus’ and 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.”

Aryabhata

A.D. 476-550

The origin of the terms ‘cosine’ and ‘tangent’ was much later. The cosine function arose from the need to compute the sine of the complementary angle.

Aryabhata called ‘kotijya’.

The name cosinus originated with Edmund Gunter. In 1674, the English Mathematician Sir Jonas Moore first used the abbreviated notation ‘cos’

COSINE AND TANGENT

Edmund Gunter

(1581 –1626)

THE TRIGONOMETRIC RATIOS

TangentTangent tantan OppositeOpposite

AdjacentAdjacent

CotangenCotangentt

cotcot AdjacentAdjacent

OppositeOpposite

SecantSecant secsec HypotenuHypotenusese

AdjacentAdjacent

CosecaCosecantnt

coseccosec HypotenuHypotenusese

OppositeOpposite

FunctionFunction Abbr.Abbr. DescriptioDescriptionn

Sine Sine sinsin OppositeOpposite

HypotenuHypotenusese

CosineCosine coscos AdjacentAdjacent

HypotenuHypotenusese

Note: The formulas provided are in respect to the picture.

The Cosecant, Secant, and Cotangent The Cosecant, Secant, and Cotangent are the Reciprocals of are the Reciprocals of the Sine, Cosine,and Tangent the Sine, Cosine,and Tangent respectively .respectively .

THE TRIGONOMETRIC VALUESAngle Angle

AA00o 3030o 4545o 6060o 9090o

sin Asin A 00 11

2211

√√22 √ √33

2211

cos Acos A 11 √√33

2211

√√2211

2200

tan Atan A 00 11

√√3311 √√33 Not Not

DefinedDefined

cosec Acosec A Not Not DefinedDefined

22 √√22 22

√√3311

sec Asec A 11 22

√√33√√22 22 Not Not

DefinedDefined

cot Acot A Not Not DefinedDefined

√√33 11 11

√√3300

HOW TO USE TRIGONOMETRY IN REAL LIFE ?

Objective : To find the angle of elevation

of a room . Knowledge Required : 1.Trigonometric Ratios

2. Trigonometric Values (acute angles)

Materials Required : 1. A meter stick

2. A measuring tape

The project given is elaborated as follows:

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 diagonal distance to your room.

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

THE MUCH AWAITED RESULT

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.

THERE’S THE ANSWER!!!

Sin A = Perpendicular

Hypotenuse

= 6 (Putting the Values)

12

Sin A = 1

2

Sin A = Sin 30o Angle of Elevation = 30o

THANK YOUTHANK YOU