Final answer:
Tangents are lines that touch a curve or circle at a single point without crossing it. They are used in geometry and trigonometry to understand the relationship between objects in circular or trigonometric motion.
Step-by-step explanation:
Tangents are used in mathematics to describe a line that touches a curve or a circle at a single point without crossing it. In geometry, a tangent line is perpendicular to the radius at the point of contact. In trigonometry, the tangent function relates the ratio of the opposite side to the adjacent side of a right triangle.
For example, in a circle, a tangent line would intersect the circle at a right angle to the radius at the point of contact. Similarly, in trigonometry, the tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.