Tangent is a trigonometric function that describes the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side, where the angle is measured in radians. It is denoted by “tan” and is calculated by dividing the length of the opposite side by the length of the adjacent side.

More formally, if we have a right triangle where one angle is θ, the tangent of θ is given by:

tan(θ) = opposite / adjacent

where opposite is the length of the side opposite to the angle θ and adjacent is the length of the side adjacent to the angle θ.

Tangent is periodic with a period of π, meaning that the tangent function repeats itself every π radians. It has vertical asymptotes at odd multiples of π/2, meaning that the tangent function approaches infinity as the angle approaches these values.