A tangent is a straight line that touches a curve at a single point without crossing it. In mathematics, particularly in geometry, tangents are often discussed in relation to circles. For example, a tangent to a circle is perpendicular to the radius drawn to the point of contact. In calculus, tangents are used to describe the slope of a curve at a specific point. The tangent line represents the instantaneous rate of change of the function at that point. This concept is essential for understanding derivatives and is foundational in the study of calculus and mathematics.