A secant line of a curve is a line that intersects two or more points on the curve. The word secant comes from the Latin secare, for to cut. In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... A spatial point is an entity with a location in space but no extent (volume, area or length). ... Latin is an ancient Indo-European language originally spoken in Latium, the region immediately surrounding Rome. ...

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 there is just one. As a consequence, one could say that the limit of the secant's slope, or direction, is that of the tangent. In mathematics, the word tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... A spatial point is an entity with a location in space but no extent (volume, area or length). ... Wikibooks Calculus has a page on the topic of Limits In mathematics, the concept of a limit is used to describe the behavior of a function as its argument either gets close to some point, or as it becomes arbitrarily large; or the behavior of a sequences elements, as... Look up Slope in Wiktionary, the free dictionary. ...

A chord is a segment of a secant line whose both ends lie on the curve. A chord of a curve is a geometric line segment whose endpoints both lie on the curve. ...

How the secant function is related to secant lines

Consider some angle θ. Draw a secant line to the unit circle (centered at the origin) that passes through the origin and through (cos θ, sin θ), the point on the unit circle at an angle of θ. The absolute value of the trigonometric secant of θ is equal to the length of a segment of the secant line running from the origin to the line x = 1. If the segment passes through the point (cos θ, sin θ), then the trigonometric secant of θ is positive; if it passes through the antipodal point, then the secant of θ is negative. Illustration of a unit circle. ... In mathematics, the origin of a coordinate system is the point where the axes of the system intersect. ... Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine and cosine. ... All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Trigonometric functions: , , , , , In mathematics, the trigonometric functions (also called circular functions) are functions of an angle; they are important when studying triangles and modeling periodic phenomena, among many other... The geometric definition of a line segment In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. ... In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite it — so situated that a line drawn from the one to the other passes through the centre of the sphere and forms a true diameter. ...

Secant approximation

A secant between x and x+h on f(x).

Consider the curve defined by y = f(x) in a Cartesian coordinate system, and consider a point P with coordinates (c, f(c)) and another point Q with coordinates (c + Δx, f(c + Δx)). Then the slope m of the secant line, through P and Q, is given by Image File history File links drawn by myself (you already guessed that . ... Fig. ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... Look up Slope in Wiktionary, the free dictionary. ...

The righthand side of the above equation is a variation of Newton's difference quotient. As Δx approaches zero, this expression approaches the derivative of f(c), assuming a derivative exists. An equation is a mathematical statement, in symbols, that two things are the same (or equivalent). ... Sir Isaac Newton, (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist, regarded by many as the greatest figure in the history of science. ... In mathematics, the derivative of a function is one of the two central concepts of calculus. ... For a non-technical overview of the subject, see Calculus. ...

See also

• Differential calculus
• Derivative
• Tangent Line

Calculus (from Latin, pebble or little stone) is a major area in mathematics where infinitesimal data yields global information. ... For a non-technical overview of the subject, see Calculus. ... In mathematics, the word tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry. ...

External links

• Secant Line from Mathworld
• Secant Lines, Tangent Lines, and Limit Definition of a Derivative
• Math Open Reference: Secant definition With interactive applet