History of Trigonometric Functions
Submitted By:
Ma. Karla Rachelle Ulibas
Student
Submitted To:
Mr. Ray-ann Buenafe
Instructor
HISTORY OF TRIGONOMETRIC FUNCTIONS
Trigonometric functions seem to have had their origins with the Greek’s investigation of the indirect measurement of distances and angles in the “celestial sphere”. (The ancient Egyptians had used some elementary geometry to build the pyramids and remeasure lands flooded by the Nile, but neither they nor the ancient Babylonians had developed the concept of angle measure). The word trigonometry, based on the Greek words for “triangle measure”, was first used as the title for a text by the German mathematician Pitiscus in A.D. 1600.
While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. The chord function was discovered by Hipparchus of Nicaea (180–125 BC) and Ptolemy of Roman Egypt (90–165 AD).
The functions sine and cosine can be traced to the jyā and koti-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic and then from Arabic to Latin.[23]
All six trigonometric functions in current use were known in Islamic mathematics by the 9th century, as was the law of sines, used in solving triangles. Al-Khwārizmī produced tables of sines, cosines and tangents. They were studied by authors including Omar Khayyám, Bhāskara II, Nasir al-Din al-Tusi, Jamshīd al-Kāshī (14th century), Ulugh Beg (14th century), Regiomontanus (1464), Rheticus, and Rheticus' student Valentinus Otho.
Madhava of Sangamagrama (c. 1400) made early strides in the analysis of trigonometric functions in terms of infinite series.
The first published use of the abbreviations 'sin', 'cos', and 'tan' is by the 16th century French mathematician Albert Girard.
In a paper published in 1682, Leibniz proved that sin x is not an algebraic function of x.
Leonhard Euler's Introductio in analysin
Ma. Karla Rachelle Ulibas
Student
Submitted To:
Mr. Ray-ann Buenafe
Instructor
HISTORY OF TRIGONOMETRIC FUNCTIONS
Trigonometric functions seem to have had their origins with the Greek’s investigation of the indirect measurement of distances and angles in the “celestial sphere”. (The ancient Egyptians had used some elementary geometry to build the pyramids and remeasure lands flooded by the Nile, but neither they nor the ancient Babylonians had developed the concept of angle measure). The word trigonometry, based on the Greek words for “triangle measure”, was first used as the title for a text by the German mathematician Pitiscus in A.D. 1600.
While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. The chord function was discovered by Hipparchus of Nicaea (180–125 BC) and Ptolemy of Roman Egypt (90–165 AD).
The functions sine and cosine can be traced to the jyā and koti-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic and then from Arabic to Latin.[23]
All six trigonometric functions in current use were known in Islamic mathematics by the 9th century, as was the law of sines, used in solving triangles. Al-Khwārizmī produced tables of sines, cosines and tangents. They were studied by authors including Omar Khayyám, Bhāskara II, Nasir al-Din al-Tusi, Jamshīd al-Kāshī (14th century), Ulugh Beg (14th century), Regiomontanus (1464), Rheticus, and Rheticus' student Valentinus Otho.
Madhava of Sangamagrama (c. 1400) made early strides in the analysis of trigonometric functions in terms of infinite series.
The first published use of the abbreviations 'sin', 'cos', and 'tan' is by the 16th century French mathematician Albert Girard.
In a paper published in 1682, Leibniz proved that sin x is not an algebraic function of x.
Leonhard Euler's Introductio in analysin