The reciprocal of a number is one over that number. For example, the reciprocal of 4 is ¼. More generally, the reciprocal of a number a is the number b such that a.b = 1. With real numbers, the reciprocal of a = 1/a for all a except 0 (1/0 has no meaning). With imaginary numbers this is true also: the reciprocal of i is 1/i, which can be expressed as i/i2 and hence as -i. (See also inverse.)
The reciprocal trigonometric functions, cosec, sec, and cot are defined as follows: cosec A = 1/sin A; sec A = 1/cos A; cot A = 1/tan A.