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 can also be expressed in terms of the sine and cosine functions, where \tan(x) = \frac\sin(x)\cos(x). The tangent function is periodic, with a period of \pi, meaning it repeats its values every \pi radians. The graph of the tangent function features vertical asymptotes, which occur where the cosine function equals zero, leading to undefined values. The function increases from negative infinity to positive infinity between these asymptotes, creating a wave-like pattern. The tangent function is widely used in various fields, including physics, engineering, and computer graphics, to model periodic phenomena.