What is the period of tan?

The period of tan refers to the periodic nature of the tangent function. In mathematics, the tangent function, commonly denoted as tan(x), relates the angle in a right triangle to the ratio of the length of the opposite side to the length of the adjacent side.

The tangent function has a periodic nature, meaning that its values repeat in a regular pattern. Specifically, the tangent function has a period of π or 180 degrees. This means that the values of tan(x) repeat every π radians or every 180 degrees.

In other words, for any given angle x, tan(x) will have the same value as tan(x + nπ), where n is an integer. For example, tan(0) = tan(180) = tan(360) = 0, tan(π/4) = tan(180+ π/4) = tan(360+ π/4) = 1, and so on.

Understanding the period of tan is essential when working with trigonometric functions, as it allows for the identification of patterns and repetitions in their values. Additionally, the period of tan can help in solving equations or determining the behavior of functions involving tangent, such as graphing its curve.