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Sine, a mathematical term, is a kind of trigonometric function. In a right triangle, the ratio of the opposite side to the hypotenuse of any acute angle ∠A is called the sine of ∠A, which is abbreviated from the English word sine, that is, the opposite side/hypotenuse of Sina = ∠ A. In ancient times, sine was the ratio of chords to chords.
In ancient times, the "string" in "hook, three strands, four strings and five" was the hypotenuse of a right triangle, and "hook" and "strand" were the two right-angled sides of a right triangle. Sine is the ratio of strands to chords, and cosine is the ratio of remaining right angles to chords. Sine = section chief/chord length Put Pythagoras' string in a circle. A chord is a line connecting two points on a circle. The largest chord is the diameter.
If the chord of a right triangle is placed on the diameter, the chord is the inverse chord of ∠A, that is, sine, and the hook is the remaining chord-cosine. According to modern theory, sine is the ratio of the opposite side to the hypotenuse of a right triangle. The modern sine formula is sin= the opposite side of a right triangle is larger than the hypotenuse, the hypotenuse is R, the opposite side is Y, and the adjacent side is A. Sina = Y/R of the included angle Ar between the hypotenuse R and the adjacent side A.
No matter what the values of a, y and r are, the sine value is always greater than or equal to 0 and less than or equal to 1, that is, 0≤sin≤ 1. Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain.
The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system. Because of the periodicity of trigonometric function, it does not have the inverse function in the sense of single-valued function. Trigonometric functions have important applications in complex numbers.
Trigonometric function is also a common tool in physics. In RT△ABC, if the acute angle A is determined, then the ratio of the opposite side to the adjacent side of the angle A is determined accordingly. This ratio is called the tangent of angle A, and is written as tanA, that is, tanA= the opposite side of angle A/the adjacent side of angle A..