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Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. [2] In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century AD), who discovered the sine function, cosine function, and versine function.
He was the first to use the abbreviations 'sin', 'cos' and 'tan' for the trigonometric functions in a treatise. [1] Girard was the first to state, in 1625, that each prime of the form 1 mod 4 is the sum of two squares. [3] (See Fermat's theorem on sums of two squares.) It was said that he was quiet-natured and, unlike most mathematicians, did ...
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
The sine and cosine functions are fundamental to the theory of periodic functions, [63] such as those that describe sound and light waves. Fourier discovered that every continuous , periodic function could be described as an infinite sum of trigonometric functions.
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 ...
His definitions of sine , cosine , versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trigonometry. He was also the first to specify sine and versine (1 − cos x ) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.
In mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century in Kerala, India by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. [1]
This ancient text uses the following as trigonometric functions for the first time: [citation needed] Sine . Cosine . Inverse sine (Otkram jya). Later Indian mathematicians such as Aryabhata made references to this text, while later Arabic and Latin translations were very influential in Europe and the Middle East. Chhedi calendar