Secant line

For information on the secant trigonometric function, see Trigonometric functions.

Common lines and line segments on a circle, including the secant line

A secant line of a curve is a line that (locally) intersects two points on the curve. The word secant comes from the Latin secare, to cut.

It can be used to approximate the tangent to a curve, at some point P. If the secant to a curve is defined by two points, P and Q, with P fixed and Q variable, as Q approaches P along the curve, the direction of the secant approaches that of the tangent at P, (assuming that the first-derivative of the curve is continuous at point P so that there is only one tangent). As a consequence, one could say that the limit as Q approaches P of the secant's slope, or direction, is that of the tangent. In calculus, this idea is the basis of the geometric definition of the derivative. A chord is the portion of a secant that lies within the curve.

A secant line on a map is a line where the projection is without distortion.

See also

• Chord
• Radius
• Diameter
• Tangent
• Circle

External links

• Weisstein, Eric W., "Secant line", MathWorld.