trigonometry

2. let’s begin the show……

3. The math of triangles
“ There is perhaps nothing which so occupies the
middle position of mathematics as trigonometry ”
- J.F. Herbart

4.  Trigonometry is derived from Greek words trigonon
(three angles) and metron ( measure).
 Trigonometry is the branch of mathematics which
deals with triangles, particularly triangles in a plane
where one angle of the triangle is 90 degrees,
Triangles on a sphere are also studied, in spherical
trigonometry.
 Trigonometry is a study of relationshiop between the
sides and angles of a triangle.
 The subject was originally devloped to solve
geometric problems involving triangles.

5. Around more than 400 years ago, the trigonometry can be traced to the
civilizations of ancient Egypt, Mesopotamia and the Indus Valley.
The first recorded use of trigonometry came from the Hellenistic
mathematician Hipparchus 150 BC , who compiled a
trigonometric table using the sine for solving triangles.
Many ancient mathematicians like Aryabhata,
Brahmagupta, Ibn Yunus and Al-Kashi made
significant contributions in this field(trigonometry).

6. ARYABHATTA
Historically, TRIGONOMETRY 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,

7. perpendicular
base
P
H
Perpendular
Hypotenuse
B
H
Base
Hypotenuse
P
B
Perpendicular
Base
 A 0 30 45 60 90
Sine 0 0.5 1/2 3/2 1
Cosine 1 3/2 1/2 0.5 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
Name of the ratio Abbreviation
Sine of  Sin 
Cosine of  Cos 
Tangent of  Tan
Cotangent of  Cot 
Secant of  Sec 
Cosecant of  Cosec 

8. sin2A + cos2A = 1
1 + tan2A = sec2A
1 + cot2A = cosec2A
sin(A+B) = sinAcosB + cosAsin B
cos(A+B) = cosAcosB – sinAsinB
tan(A+B) = (tanA+tanB)/(1 – tanAtan B)
sin(A-B) = sinAcosB – cosAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A-B)=(tanA-tanB)(1+tanAtanB)
sin2A =2sinAcosA
cos2A=cos2A - sin2A
tan2A=2tanA/(1-tan2A)
sin(A/2) = ±{(1-cosA)/2}
Cos(A/2)= ±{(1+cosA)/2}
Tan(A/2)= ±{(1-cosA)/(1+cosA)}
•There are 2л radian in a full rotation once a
round circle.
•There are 360 in a full rotation
2л 360 л 180
•How to convert degree to radian , and radian to degree.
degree = radian
180 л
r
1 radian
r

9. Sin /
Cosec 
P
(pandit)
H
(har)
Cos /
Sec 
B
(badri)
H
(har)
Tan /
Cot 
P
(prasad)
B
(bole)
• To learn trigonometric ratios you
can use any one

10. Graphing Trig Functions
Y= tanx

11. How do engineers make an exact structure of the
blueprint?
How do we measure the
distance of stars?
How do pilots find their way in the
sky where traffic signs cannot be
placed?

12. • In architecture, trigonometry plays a
massive role in the compilation of
building plans.
• Trigonometry is the mathematics of
sound and music.
• The technique of triangulation is used
to measure the distance to nearby stars.
Sine i
Sine r
= Refractive index
Some monuments built on rule of trigonometry

13. How to calculate the values of trigonometric
functions

14. Among the scientific fields that make use of trigonometry are
these:
In all the fields you will find uses of trigonometry.

15. HEIGHT AND DISTANCES