This document is a slideshow presentation on trigonometry given by Anjaya Bhattarai. The presentation provides definitions of trigonometry, a brief history of the subject, descriptions of right triangles and trigonometric ratios. It also covers Pythagoras' theorem, its proof, and uses of trigonometry. The objective is to clarify basic trigonometry concepts and solve any confusion. In conclusion, trigonometry measures triangle sides and angles through important formulas, and it has many applications in fields like engineering, navigation, and more.

1. DONE BY:ANJAYA BHATTARAI
CLASS:7 ‘A’
ROLL NO:2
Submitted to: mathematics department
Kanjirowa national school
Supervised by: janak singh saud

2. Acknowledgement
 I would like to thank the mathematics department
for giving me the opportunity to present this slide
show on exploration of trigonometry program. I
would like to thank my brother who gave me time
to do this work . I would like to thank my parents
who provided all the materials I wanted.

3. Objective of this presentation
 It will help us to know the basic concept of
trigonometry.
 It will solve out all the confusion about the basic
concept of trigonometry.
 It will clarify that the basic concepts of
trigonometry are not hard.

4. What is trigonometry?
 The branch of mathematics dealing with the
relations of the sides and angles of triangles and
with the relevant functions of any angles.
 Trigonometry is a branch of mathematics that
studies relationships between the sides and angles
of triangles.
 Trigonometry is the branch of mathematics that
include relationships involving lengths and angles
of triangles.

5. History of trigonometry
 Sumerian astronomers studied angle
measure, using a division of circles into 360
degrees.They, and later the Babylonians,
studied the ratios of the sides
of similar triangles and discovered some
properties of these ratios but did not turn
that into a systematic method for finding
sides and angles of triangles. The ancient
Nubians used a similar method.

6. Continue……..
 In the 3rd century BC, Hellenistic
mathematicians such
as Euclid and Archimedes studied the properties
of chords and inscribed angles in circles, and they
proved theorems that are equivalent to modern
trigonometric formulae, although they presented
them geometrically rather than algebraically. In 140
BC, Hipparchus (from Nicaea, Asia Minor) gave the
first tables of chords, analogous to modern tables of
sine values, and used them to solve problems in
trigonometry and spherical trigonometry. In the 2nd
century AD, the Greco-Egyptian
astronomer Ptolemy (from Alexandria, Egypt)

7. Cont…….
printed detailed trigonometric tables (Ptolemy's table
of chords) in Book 1, chapter 11 of
his Almagest.Ptolemy used chord length to define his
trigonometric functions, a minor difference from
the sine convention we use today. (The value we call
sin(θ) can be found by looking up the chord length for
twice the angle of interest (2θ) in Ptolemy's table, and
then dividing that value by two.) Centuries passed
before more detailed tables were produced, and
Ptolemy's treatise remained in use for performing
trigonometric calculations in astronomy throughout
the next 1200 years in the medieval Byzantine, Islamic,
and, later, Western European worlds.

8. RIGHT ANGLED TRIANGLE
 Adjacent[base]is next to[adjacent to] to reference
angle.
 Opposite [perpendicular] is opposite to the
reference angle
 Hypotenuse is the longest side

9. PYTHAGORAS THEOREM

10. PHYTHAGORAS THEOREM PROOF
 Angle AB is the hypotenuse.
 Angle BC is the base.
 Angle AC is the perpendicular

11. TRYGONOMETRICAL RATIOS

12. USES OF TRYGONOMETRY
Fourier series
Fourier transforms
Statics,including mathematical
psychology
Number theory
Solving non-trigonometric
equations

13. Conclusion
 Trigonometry is the branch of mathematics which
deals with the measurement of sides and angles of
a triangle. There are many formulas in
trigonometry. It has many uses. It is used in our
daily life. It is a very important topic

14. THANK YOU
HOPE YOU ALL LIKED
THE PRESENTATION