History of Trigonometry PDF

TRIGONOMETRY HISTORY…TERMS… What is Trigonometry? TRIGONOMETRY – is the branch of Mathematics that deals with the properties and applications of ratios associated 3 GREEK with angles WORDS OF TRIGONOMETRY TRI - GONIA – CORNER / METRON - THREE ANGLE MEASUR...

TRIGONOMETRY HISTORY…TERMS… What is Trigonometry? TRIGONOMETRY – is the branch of Mathematics that deals with the properties and applications of ratios associated 3 GREEK with angles WORDS OF TRIGONOMETRY TRI - GONIA – CORNER / METRON - THREE ANGLE MEASURE  APPLIED IN THE FIELDS OF : SURVEYING NAVIGATION ASTRONOMY FOUND IN THE STUDY OF : TIDES ( RISE AND FALL ) BUSINESS CYCLES BIOLOGICAL RHYTHMS ( HEARTBEATS AND BRAIN WAVES)  KINDS OF TRIGONOMETRY 1.PLANE TRIGO – studies the properties of triangles in a plane and its two dimension. 2.SPHERICAL TRIGO – concerned with relations that exist among the sides and angles of a spherical triangle. A spherical triangle is a portion of the surface of a sphere bounded by the arcs of three great circlesmwhich  HISTORY OF TRIGONOMETRY TRIGO GREEK ASTRONOMY ASTRONOMY – study of heavenly bodies. From the earth, they saw that the planets seemed to move in an irregular way on the surface of the large sphere which they called the CELESTIAL SPHERE. PERSONS BEHIND TRIGONOMETRY HIPPARCHUS OF NICAEA Mathematician and Astronomer He is considered the founder of Trigonometry He was the first to construct an accurate table of ratios of a triangle. He created the first accurate star map “Greatest of the Greek astronomers” MENELAUS OF MENELAUS OF ALEXANDRIA ALEXANDRIA AND CLAUDE PTOLEMY They made significant contributions to the study of spherical trigonometry. CLAUDE PTOLEMY He constructed a table of trigonometric ratios for angles between 0using the half a degree. Ptolemy’s Book ( ALMAGEST ) – exerted a profound influence on Astronomy and Trigonometry Geocentric Theory – this theory puts the earth at the center of the universe with the sun , moon and planets revolving around it, NASIR EDDIN al - Tusi He wrote the first treatise on trigonometry that was independent of the topic astronomy  DEATH OF PTOLEMY ROMAN EMPIRE fell and EUROPE experienced a period known as the DARK AGE HINDUS AND ARABS – they were the ones who introduced the concepts of TANGENT and COTANGENT. They concstructed tables of half chords which are equivalent to sines and discovered many theorem. RENAISSANCE – revival of learning. GEORG von PURBACH and His pupil JOHANN MULLER They spearheaded the revival of study of Trigo in Europe GEORG von PURBACH - as an Austrian astronomer, mathematician and instrument maker, best known for his streamlined presentation of Ptolemaic astronomy in the Theoricae Novae Planetarum. He used Arabic numerals to prepare a table of sines of unprecendented accuracy, advancing the mecahnics of Trigo past the Greek and Arabic marks JOHANNES MULLER von KONIGSBERG He is known as REGIOMONTANUS He introduced the use of Arabic algebraic and trigonometric methods, reproducing the tables in printed form. He also translated the Almagest from Greek to Latin He wrote a book entiled “ De Triangulis” GEORG JOACHIM ISERIN He is known as RHAETICUS He is a German Astronomer and Mathematician The first to relate the trigonometric functions to angles rather than to the arcs of circles and prepared the BEST TRIGONOMETRIC TABLE during his time. He was the first to defined the SIX CIRCULAR FUNCTIONS as the ratios of the sides of a right triangle. FRANCOIS VIETE He simplified the exposition of trigonometry through his systematic use of Algebra. He further extended the circular function table ( up to seven places for every second ) which was prepared by Rheticus BARTHOLOMAEUS PITISCUS He wrote the first textbook to bear the title “Trigonometry” WILLIAM OUGHTRED He published a textbook on Math in which he introduced the Multiplication sign ( x ). The abbreviations for sine ( sin ) cosine ( cos ) tangent ( tan ) LIONARD EULER The most prolific writer of Mathematical subjects of all time. He wrote a book entitled “Introductio in Analysin Infinitorum”where trigonometric functions where first defined as ratios rather than lengths.This book became a standard reference in CALCULUS. Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions and the analytic theory of continued fractions. LIONARD EULER ABRAHAM de MOIVRE His main contribution to Math is in the field of Trigo.One of the two important theorems which bears his name is the famous equation Cos nx + 𝑖 sin nx = ( cos x + 𝑖 sin x ) n Where n is a rational number and 𝑖 2 =-1 His work entitled “Miscellanea Analytica” is a treatise on Trigonometry theorems with special reference to infinite series.