Tangent function

The tangent function relates to the angles of a right triangle, specifically the ratio of the length of the side opposite the angle to the length of the side adjacent to it. In a unit circle, tangent of an angle is the ratio of the y-coordinate to the x-coordinate of the point on the circle corresponding to that angle. It is useful in geometry, engineering, and physics for modeling oscillations, waves, and rotations. The tangent function varies periodically, with values that can become very large or small, reflecting its cyclical nature.