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Secant line. In geometry, a secant is a line that intersects a curve at a minimum of two distinct points. [1] The word secant comes from the Latin word secare, meaning to cut. [2] In the case of a circle, a secant intersects the circle at exactly two points. A chord is the line segment determined by the two points, that is, the interval on the ...
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions.
Secant is a term in mathematics derived from the Latin secare ("to cut"). It may refer to: a secant line, in geometry the secant variety, in algebraic geometry secant (trigonometry) (Latin: secans), the multiplicative inverse (or reciprocal) trigonometric function of the cosine the secant method, a root-finding algorithm in numerical analysis, based on secant lines to graphs of functions a ...
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, [1][2][3][4][5] antitrigonometric functions[6] or cyclometric functions[7][8][9]) are the inverse functions of the trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [10] and are used ...
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years.
Chord (geometry) A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for ...
For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: Intersecting secants theorem: For a point outside a circle and the intersection points of a secant line with the following statement is true: , hence the product is independent of line . If is tangent then and the statement is the tangent-secant theorem. Intersecting chords theorem: For ...
A standard method of evaluating the secant integral presented in various references involves multiplying the numerator and denominator by sec θ + tan θ and then using the substitution u = sec θ + tan θ. This substitution can be obtained from the derivatives of secant and tangent added together, which have secant as a common factor.