In geometry, a secant is a line that intersects a curve or surface at two or more points. More specifically, a secant line is a straight line that passes through any two points on a curve or surface, including a line that intersects a circle at two distinct points.
A secant line is different from a tangent line, which intersects a curve or surface at only one point and is perpendicular to the curve or surface at that point.
The term «secant» is derived from the Latin word «secare,» which means «to cut.» In geometry, a secant line is said to cut a curve or surface, because it intersects it at two or more points, thereby dividing it into two or more sections. The study of secants and tangents is an important part of differential geometry and calculus.
Here are a few additional points to consider regarding secants in geometry:
- The segment of the secant line between the two points of intersection with the curve or surface is called a chord. Chords play an important role in the study of circles, particularly in the calculation of arc length and angles subtended by chords.
- If the curve or surface is a function graph, then a secant line between two points on the curve represents the average rate of change (slope) of the function over that interval.
- Secant lines can be used to estimate the value of a function at a point between the two points of intersection. This is known as linear interpolation and is often used in numerical analysis and data science.
- In trigonometry, the secant function is defined as the reciprocal of the cosine function. In this context, the secant is used to describe the ratio between the hypotenuse and adjacent side of a right triangle.
- Secants can also be used in the study of conic sections (such as ellipses, hyperbolas, and parabolas) to determine the points of intersection with other curves or surfaces.