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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. Spherical trigonometry. Arithmetic: Simple continued fractions. Algebra: Solutions of simultaneous ...
According to one convention, the functions jyā and koti-jyā are respectively denoted by "Rsin" and "Rcos" treated as single words. [1] Others denote jyā and koti-jyā respectively by "Sin" and "Cos" (the first letters being capital letters in contradistinction to the first letters being small letters in ordinary sine and cosine functions).
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 cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-". [32] With these functions, one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines. [33]
One way to remember the letters is to sound ... with n = 0, 1, ..., 4 for sine and n = 4, 3, ..., 0 for cosine, ... An alternate way to remember the letters for Sin ...
The sine and the cosine functions, for example, are used to describe simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string. The sine and cosine functions are one-dimensional projections of uniform circular motion.
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six ...
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