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For the second one, the text states: "We multiply the sine of each of the two arcs by the cosine of the other minutes. If we want the sine of the sum, we add the products, if we want the sine of the difference, we take their difference". [45] He also discovered the law of sines for spherical trigonometry: [41]
Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's ...
Contains the earliest tables of sine, cosine and versine values, in 3.75° intervals from 0° to 90°, to 4 decimal places of accuracy. Contains the trigonometric formula sin( n + 1) x − sin nx = sin nx − sin( n − 1) x − (1/225)sin nx .
Fig. 1a – Sine and cosine of an angle θ defined using the unit circle Indication of the sign and amount of key angles according to rotation direction Trigonometric ratios can also be represented using the unit circle , which is the circle of radius 1 centered at the origin in the plane. [ 37 ]
[8]: 14 Because al-Khwarizmi was the first person to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), [9] he has been described as the father [10 ...
Among his many contributions, he discovered infinite series for the trigonometric functions of sine, cosine, arctangent, and many methods for calculating the circumference of a circle. One of Madhava's series is known from the text Yuktibhāṣā , which contains the derivation and proof of the power series for inverse tangent , discovered by ...
ca. 1000 – Law of sines is discovered by Muslim mathematicians, but it is uncertain who discovers it first between Abu-Mahmud al-Khujandi, Abu Nasr Mansur, and Abu al-Wafa. ca. 1100 – Omar Khayyám "gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections."
In his paper, [4] Funkhouser locates the work of Girard in the history of the study of equations using symmetric functions. In his work on the theory of equations , Lagrange cited Girard. Still later, in the nineteenth century, this work eventuated in the creation of group theory by Cauchy , Galois and others.