Tangent is a trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle.
In a right triangle, tan(θ) = opposite/adjacent = sin θ/cos θ. Tangent is periodic with period π and has vertical asymptotes where cos θ = 0. In calculus, the tangent line at a point on a curve represents the instantaneous direction and slope.
The tangent function developed later than sine and cosine. The term "tangent" comes from Latin "tangere" (to touch). The function was studied by Islamic mathematicians like Abu al-Wafa in the 10th century.