Pronunciation: (sīn),[key] —n. 1. Trig. a. (in a right triangle) the ratio of the side opposite a given acute angle to the hypotenuse.
b. (of an angle) a trigonometric function equal to the ratio of the ordinate of the end point of the arc to the radius vector of this end point, the origin being at the center of the circle on which the arc lies and the initial point of the arc being on the x-axis. Abbr.: sin
2. Geom.(originally) a perpendicular line drawn from one extremity of an arc of a circle to the diameter that passes through its other extremity.
3. Math.(of a real or complex number x) the function sin x defined by the infinite series x - (x3/3!) + (x5/5!) - + … , where ! denotes factorial. Cf. cosine (def. 2), factorial (def. 1).