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So I'm interested in integrating the square root of (a^2 - y^2), dy. In 830, Habash al-Hasib al-Marwazi produced the first table of cotangents. [30] [31] Muhammad ibn Jābir al-Harrānī al-Battānī (Albatenius) (853-929) discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants for each degree from 1° to 90°. [31] He was also responsible for formulating and establishing a number of important trigometrical relationships, such as: By the 10th century, in the work of Abū al-Wafā' al-Būzjānī, Islamic mathematicians were using all six trigonometric functions. [32] Abu al-Wafa had sine tables in 0.25° increments, to 8 decimal places of accuracy, and accurate tables of tangent values. [32] He also developed the following trigonometric formula: Abū al-Wafā also established the angle addition identities, e.g. sin (a + b), and discovered the law of sines for spherical trigonometry: [30] In the late 10th to early 11th centuries, the Egyptian astronomer Ibn Yunus performed many careful trigonometric calculations and demonstrated the following trigonometric identity: Al-Jayyani (989–1079) of Al-Andalus (Islamic Spain) wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry " in its modern form. [33] The book of unknown arcs of a sphere "contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle."

Pages: 422

Publisher: Nabu Press (January 5, 2014)

ISBN: 1295460297

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