Tangent (trigonometry) definition of Tangent (trigonometry) in the Free Online Encyclopedia.

tangent, in mathematics.

1 In geometry, the tangent to a circle circle, closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
..... Click the link for more information. or sphere is a straight line that intersects the circle or sphere in one and only one point. For other curves and surfaces the tangent line at a given point P is defined as the limiting position, if such a limit limit, in mathematics, value approached by a sequence or a function as the index or independent variable approaches some value, possibly infinity. For example, the terms of the sequence 1-2, 1-4, 1-8, 1-16, … are obviously getting smaller and smaller; since,
..... Click the link for more information. exists, of a secant line through P and another point P′ on the curve or surface as P′ is allowed to approach P. The tangent plane to a surface at a point is the plane in which every line in the plane that passes through the point is a tangent line to the surface at that point. The study of tangent lines and planes usually requires the concepts of the calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit —the notion of tending toward, or approaching, an ultimate value.
..... Click the link for more information. and is included within the scope of differential geometry r moves along a curve at arc length s from some fixed point, then t = dr/ds is a unit tangent vector to the curve at r. The normal vector n
..... Click the link for more information. .

2 A trigonometric function. See trigonometry trigonometry [Gr.,=measurement of triangles], a specialized area of geometry concerned with the properties of and relations among the parts of a triangle. Spherical trigonometry is concerned with the study of triangles on the surface of a sphere rather than in the
..... Click the link for more information. .

tangent

1. a geometric line, curve, plane, or curved surface that touches another curve or surface at one point but does not intersect it

2. (of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the opposite side to that of the adjacent side; the ratio of sine to cosine

3. Music a part of the action of a clavichord consisting of a small piece of metal that strikes the string to produce a note

tangent [′tan·jənt]

(mathematics)

A line is tangent to a curve at a fixed pointPif it is the limiting position of a line passing throughPand a variable point on the curveQ,asQapproachesP.

The function which is the quotient of the sine function by the cosine function. Abbreviated tan.

The tangent of an angle is the ratio of its sine and cosine. Abbreviated tan.

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