This document provides an overview of trigonometry including its history, applications, basic concepts, and trigonometric tables. It discusses how trigonometry originated from Babylonian, Greek, Indian and Arabic mathematics and astronomy. It explains that trigonometry is commonly used to calculate heights, distances, and positions in navigation, engineering, and astronomy. The basic concepts covered are the definitions of the sine, cosine, and tangent functions for right triangles, Pythagorean theorem, and trigonometric identities. Trigonometric tables are also mentioned.

1. Trigonometry

2. Contents of the Presentation
 History of Trigonometry
 Where it is used
 Basic concepts in trigonometry
 Trigonometric table
 Trigonometric identities

3. History of Trigonometry
 The complex origins of trigonometry are embedded in
the history of the simple word "sine," a mistranslation
of an Arabic transliteration of a Sanskrit mathematical
term. The complex etymology of "sine" reveals
trigonometry's roots in Babylonian, Greek, Hellenistic,
Indian, and Arabic mathematics and astronomy.
 Although trigonometry now is usually taught beginning
with plane triangles, its origins lie in the world of
astronomy and spherical triangles. Before the
sixteenth century, astronomy was based on the notion
that the earth stood at the centre of a series of
nested spheres. To calculate the positions of stars or
planets, one needed to use concepts we now refer to
as trigonometry.

4. Where it is used in daily life
 Trigonometry is commonly used in finding the height of
towers and mountains.
 It is used in navigation to find the distance of the shore
from a point in the sea.
 It is used in finding the distance between celestial
bodies.
 It is used in oceanography in calculating the height of
tides in oceans.

5. Basic concepts in Trigonometry
 Right Angle Triangle :
Right angle triangle is a triangle in which one of its
interior angle is 90 degree. The opposite side of the
right angle triangle is hypothesis and the other two
sides are adjacent and opposite. Basic sin,cos and tan
functions are as follows,
Name Ratio Notation
Sine Opposite/hypotenuse Sin(0)
Cosine Adjacent/hypotenuse Cos(0)
Tangent Opposite/adjacent Tan(0)
Cosecant(1/Sine) Hypotenuse/Opposite Cosec(0) or csc(0)
Secant(1/Cosine) Hypotenuse/adjacent Sec(0)
Contagent(1/Tangent) Adjacent/opposite Cot(0)

6. Basic concepts of
Trigonometry
 Pythagoras Theorem:
Pythagoras theorem is used to find the sides of
The right angle. Pythagoras theorem is,
(Hypotenuse)2=(Adjacent)2 + (Opposite)2
 Triangle Identities:
Triangle identities are the function. There are some
identities which are true for right angle triangles and
some are true for all triangles.

7. Trigonometric table

8. Created by
Ashwin Rao