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The text's 12th-century Latin translator used the Latin equivalent for "bosom", sinus. [6] When jyā became sinus, it has been suggested that by analogy kojyā became co-sinus. However, in early medieval texts, the cosine is called the complementi sinus "sine of the complement", suggesting the similarity to kojyā is coincidental. [7]
Indian mathematicians made early contributions to the study of the concept of zero as a number, [5] negative numbers, [6] arithmetic, and algebra. [7] In addition, trigonometry [8] was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. [9]
In radians, one would require that 0° ≤ x ≤ π/2, that x/π be rational, and that sin(x) be rational. The conclusion is then that the only such values are sin(0) = 0, sin(π/6) = 1/2, and sin(π/2) = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. [2] The theorem extends to the other trigonometric functions ...
The Bhagavad Gita (/ ˈ b ʌ ɡ ə v ə d ˈ ɡ iː t ɑː /; [1] Sanskrit: भगवद्गीता, IPA: [ˌbʱɐɡɐʋɐd ˈɡiːtɑː], romanized: bhagavad-gītā, lit. 'God's song'), [a] often referred to as the Gita (IAST: gītā), is a Hindu scripture, dated to the second or first century BCE, [7] which forms part of the epic Mahabharata.
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 ...
For the angle α, the sine function gives the ratio of the length of the opposite side to the length of the hypotenuse.. To define the sine and cosine of an acute angle , start with a right triangle that contains an angle of measure ; in the accompanying figure, angle in a right triangle is the angle of interest.
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In this right triangle: sin A = a/h; cos A = b/h; tan A = a/b. Trigonometric ratios are the ratios between edges of a right triangle. These ratios depend only on one acute angle of the right triangle, since any two right triangles with the same acute angle are similar. [31]
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