# reciprocal

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* /*i*^{ 2} 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*.