1. TRIGONOMETRY
Prepared By :-
name : Md.Abdullah Ali
Class : X H

2. The word ‘Trigonometry’ is derived from the
Greek words ‘tri’(meaning three),’gon’
(meaning sides) and ‘metron’(meaning
measure).
Trigonometry is the study of relationships
between the sides and angles of a
triangle.

3.  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.

4.  Sine(sin) opposite side/hypotenuse
 Cosine(cos) adjacent side/hypotenuse
 Tangent(tan) opposite side/adjacent side
 Cosecant(cosec) hypotenuse/opposite side
 Secant(sec) hypotenuse/adjacent side
 Cotangent(cot) adjacent side/opposite side

5.  sinθ=b/a
 cosθ=c/a
 tanθ=b/c
 cosecθ=a/b
 secθ=a/c
 cotθ=c/b

6. 0 30 45 60 90
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

7.  The line of sight is a straight line along which an observer
observes an object. It is an imaginary line that stretches
between observer's eye and the object that he is looking at.
If the object being observed is above the horizontal, then the
angle between the line of sight and the horizontal is called
angle of elevation. If the object is below the horizontal, then
the angle between the line of sight and the horizontal is
called the angle of depression.

8.  sin2A+cos2A=1
 1+tan2A=sec2A
 1+cot2A=cosec2A
 sin (A+B)= sinAcosB + cosAsinB
 cos (A+B) = cosAcosB - sinAsinB
 tan(A+B) = (tanA + tanB) / (1-tanAtanB)
 sin(A-B) = sinAcosB - cosAsinB
 cos(A-B) = cosAcosB + sinAsinB
 tan(A-B) = (tanA - tanB)(1 + tanAtanB)
 sin2A=2sinAcosA
 cos2A=cos2A-sin2A

9.  cosθ= sin(90- θ)
 sinθ= cos(90- θ)
 cotθ= tan(90- θ)
 secθ= cosec(90- θ)
 cosecθ= sec(90- θ)
 tanθ= cot(90- θ)

10.  This field of mathematics can be applied in astronomy , navigation ,
music theory , optics , analysis of financial markets , electronics ,
probability theory, statistics , biology , medical imaging , pharmacy ,
chemistry , number theory , seismology , meteorology ,
oceanography , many physical sciences , land surveying and
geodesy , architecture , phonetics , economics , electrical
engineering , mechanical engineering , civil engineering ,
computer graphics , cartography , crystallography and game
development.

11.  Since ancient times trigonometry was used in astronomy.
 The technique of triangulation is used to measure the distance
between nearby stars.
 In 240 B.C , a mathematician named Eratosthenes discovered the
radius of the Earth using trigonometry and geometry.
 In 2001 , a group of European astronomers did an experiment that
started in 1997 about the distance of Venus from the Sun. Venus was
about 105,000,000 kilometres away from the Sun.

12.  Many modern buildings have beautifully curved surfaces.
 Making these curves out of steel , stone , concrete or glass is
extremely difficult , if not impossible.
 One way around to address this problem is to piece the surface
together out of many flat panels , each sitting at an angle to the
one next to it , so that all together they create what looks like a
curved surface.
 The more regular these shapes , the easier the building process.
 Regular flat shapes like squares , pentagons and hexagons , can be
made out of triangles , and so trigonometry plays an important role
in architecture.

13.  Trigonometry plays an important role in navigation . It assists
with the calculation of the coordinates of a specific point on
a Cartesian plane. This is also used to represent the directions
of the four compass points: north, south, east and west,
where it is used for finding the bearing of an object from
another. Trigonometry is also used in navigating from one
place to another on a straight line. This can therefore also tell
you the distance from you, to your destination.

14.  www.google.com
 www.wikipedia.org
 www.slideshare.net
 math.tutorvista.com
 www.khanacademy.org
 www.meritnation.com

15. THE END