Trigonometry deals with calculating distances and heights using mathematical techniques. It originated in ancient Greece and Egypt for purposes like astronomy and geography. Hipparchus is considered one of the founders of trigonometry for developing quantitative models of celestial motions. Trigonometry is now widely used in fields like calculus, physics, engineering, and more. It allows calculating inaccessible lengths like heights and widths using angles of elevation, depression, and trigonometric functions like sine, cosine, and tangent.

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3. Trigonometry is a branch of Mathematics that deals with the distances or
heights of objects which can be found using some mathematical techniques.
The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three) ,
‘gon’ (meaning sides) and ‘metron’ (meaning measure).
Historically, it was developed for astronomy and geography, but scientists
have been using it for centuries for other purposes, too. Besides other fields
of mathematics, trigonometry is used in physics, engineering, and chemistry.
Within mathematics, trigonometry is used primarily in calculus (which is
perhaps its greatest application), linear algebra, and statistics. Since these
fields are used throughout the natural and social sciences, trigonometry is a
very useful subject to know.
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4. Some historians say that trigonometry was invented by
Hipparchus, a Greek mathematician. He also introduced the
division of a circle into 360 degrees into Greece.
Hipparchus is considered the greatest
astronomical observer, and by some the
greatest astronomer of antiquity. He was the
first Greek to develop quantitative and
accurate models for the motion of the Sun and
Moon. With his solar and lunar theories and
his numerical trigonometry, he was probably
the first to develop a reliable method to predict
solar eclipses.
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5. History of trigonometry
 The origins of trigonometry can be traced to the civilizations of
ancient Egypt, Mesopotamia and the Indus Valley, more than
4000 years ago.
 Some experts believe that trigonometry was originally
invented to calculate sundials, a traditional exercise in the
oldest books
 The first recorded use of trigonometry came from the
Hellenistic mathematician Hipparchus circa 150 BC, who
compiled a trigonometric table using the sine for solving
triangles.
 The Sulba Sutras written in India, between 800 BC and
500 BC, correctly compute the sine of π/4 (45°) as 1/√2 in
a procedure for circling the square (the opposite of
squaring the circle).

6. B A
C
Sin /
Cosec 
P
(pandit)
H
(har)
Cos /
Sec 
B
(badri)
H
(har)
Tan / Cot

P
(prasad)
B
(bole)
BASE (B)
PERPENDICULAR (P)

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00 300 450 600 900
Sine 0 1/2 1/2 3/2 1
Cosine 1 3/2 1/2 1/2 0
Tangent 0 1/ 3 1 3 Not
defined
Cosecant Not
defined
2 2 2/ 3 1
Secant 1 2/ 3 2 2 Not
defined
Cotangent Not
defined
3 1 1/ 3 0

8. Sin2  + Cos2  = 1
• 1 – Cos2  = Sin2 
• 1 – Sin2  = Cos2 
Tan2  + 1 = Sec2 
• Sec2  - Tan2  = 1
• Sec2  - 1 = Tan2 
Cot2  + 1 = Cosec2 
• Cosec2  - Cot2  = 1
• Cosec2  - 1 = Cot2 
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9. Applications
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Measuring inaccessible lengths
Height of a building (tree,
tower, etc.)
Width of a river (canyon, etc.)

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 Angle of Elevation –
It is the angle formed by the line of sight with the horizontal when it is
above the horizontal level, i.e., the case when we raise our head to
look at the object.

A
HORIZONTAL LEVEL
ANGLE OF ELEVATION

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 Angle of Depression –
It is the angle formed by the line of sight with the horizontal when it is
below the horizontal level, i.e., the case when we lower our head to
look at the object.
 A
HORIZONTAL LEVEL
ANGLE OF DEPRESSION

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h = ?
HORIZONTAL LEVEL


It is an instrument which is used to measure the
height of distant objects using trigonometric
concepts.
Here, the height of the tree using T. concepts,
h = tan  *(x)
‘x’
units

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14. 1. The angle of elevation of the top of a tower from a point At the
foot of the tower is 300 . And after advancing 150mtrs Towards
the foot of the tower, the angle of elevation becomes 600 .Find
the height of the tower?
150
h
d
30 60
mh
h
hh
hh
hh
dofvaluethengSubstituti
hd
From
hdFrom
d
h
Tan
d
h
Tan
9.129732.1*75
31502
31503
31503
)1503(3
..........
)150(3
)2(
3)1(
)2(
150
360
)1(
3
1
30












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2.The angle of elevation of the top of a tower from a point on
the ground, which is 30 m away from the foot of the tower is
30°. Find the height of the tower.
Therefore, the height of the tower is

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3. A circus artist is climbing a 20 m long rope,
which is tightly stretched and tied from the top of a
vertical pole to the ground. Find the height of the
pole, if the angle made by the rope with the ground
level is 30 °.Sol:- It can be observed from the figure that AB is
the pole.
In ΔABC,
Therefore, the height of the pole is 10 m.

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Trigonometry begins in the right triangle, but it
doesn’t have to be restricted to triangles. The
trigonometric functions carry the ideas of triangle
trigonometry into a broader world of real-valued
functions and wave forms.
Trig functions are the relationships amongst various
sides in right triangles.
The enormous number of applications of trigonometry
include astronomy, geography, optics, electronics,
probability theory, statistics, biology, medical imaging
(CAT scans and ultrasound), pharmacy, seismology,
land surveying, architecture.
I get it!

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