What is a period in math terms?

In math terms, the period of a function is the smallest interval over which the values of the function recur. For example, the sine function, sin(x), has a period of 2pi, as sin(x + 2pi) = sin(x) for all values of x.

Not all mathematical functions have periods. Some functions, such as f(x) = x, have no recurring values; every value of x gives a different value of f(x). The most well-known periodic functions are the trigonometric functions sine and cosine, both of which have a period of 2pi. The tangent function, tan(x) = sin(x)/cos(x), is also periodic, with a period of pi.