The tangent function is a fundamental concept in trigonometry, defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is commonly represented as tan(θ), where θ is the angle of interest. The tangent function is periodic, with a period of π, meaning it repeats its values every π radians. In the unit circle, the tangent function can also be understood as the y-coordinate divided by the x-coordinate of a point on the circle. The function has vertical asymptotes where the cosine function is zero, leading to undefined values at those points.