TRIGONOMETRYDONE BY:ANJAYA BHATTARAI

CLASS:7 ‘A’ROLL NO:2

Submitted to: mathematics departmentKanjirowa national school

Supervised by: janak singh saud

AcknowledgementI 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.

Objective of this presentationIt 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.

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.

History of trigonometrySumerian 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.

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)

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.

RIGHT ANGLED TRIANGLEAdjacent[base]is next to[adjacent to] to

reference angle.Opposite [perpendicular] is opposite to

the reference angleHypotenuse is the longest side

PYTHAGORAS THEOREM

PHYTHAGORAS THEOREM PROOFAngle AB is the hypotenuse.Angle BC is the base.Angle AC is the perpendicular

TRYGONOMETRICAL RATIOS

USES OF TRYGONOMETRYFourier seriesFourier transformsStatics,including mathematical psychologyNumber theorySolving non-trigonometric equations

ConclusionTrigonometry 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

THANK YOU HOPE YOU ALL LIKED THE PRESENTATION