Trigonometry is the branch of mathematics dealing with relationships between sides and angles of triangles. The document traces the origins of common trigonometric functions like sine, cosine, and tangent from ancient Indian and Greek mathematicians. It then explains how trigonometric ratios are used to calculate the angle of elevation of a room by measuring the wall length and diagonal distance and applying the sine ratio formula.

1. USE OF
TRIGONOMETRY IN
REAL LIFE
SUPREIYA
CLASS : X - A

2. 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.

3. ORIGIN OF ‘SINE’
“Trigonometry is not the work of any one person or nation. Its
history spans thousands of years and has touched every major
civilization .”
 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 ’ .
Aryabhata
A.D. 476-550

4. COSINE AND TANGENT
 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’
Edmund Gunter
(1581 –1626)

5. THE TRIGONOMETRIC RATIOS
Abbr.
Descriptio
n
Sine
sin
Opposite
Cosine
cos
Tangent
tan
Cotangent
The Cosecant, Secant, and Cotangent
are the Reciprocals of
the Sine, Cosine,and Tangent
respectively .
Function
cot
Secant
Note: The formulas provided
are in respect to the picture.
sec
Cosecan cosec
t
Hypotenus
e
Adjacent
Hypotenus
e
Opposite
Adjacent
Adjacent
Opposite
Hypotenus
e
Adjacent
Hypotenus
e

6. THE TRIGONOMETRIC VALUES
Angle A
0o
30o
45o
60o
90o
sin A
0
1
1
√3
1
1
2
√3
√2
1
2
1
0
0
2
1
√2
1
2
√3
√3
2
√2
2
2
√2
√3
2
√3
√3
1
1
cos A
tan A
cosec A
sec A
cot A
Not
Defined
1
Not
Defined
√3
Not
Defined
1
Not
Defined
0

7. HOW TO USE
TRIGONOMETRY IN REAL
The LIFE given is elaborated as follows:
project ?

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

8. 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 !!

9. 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.

10. THERE’S THE ANSWER!!!
 Sin A = Perpendicular
Hypotenuse
=
(Putting the Values)
6
12
Sin A
= 1
2
Sin A = Sin 30
o
Angle of Elevation = 30o

11. THANK
YOU