# tangent

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Related to Tangent (trigonometry): Tangent function

## tangent,

in mathematics. 1 In geometry, the tangent to a circlecircle,
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.
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 limitlimit,
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, if enough
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 calculuscalculus,
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.
and is included within the scope of differential geometrydifferential geometry,
branch of geometry in which the concepts of the calculus are applied to curves, surfaces, and other geometric entities. The approach in classical differential geometry involves the use of coordinate geometry (see analytic geometry; Cartesian coordinates),
. 2 A trigonometric function. See trigonometrytrigonometry
[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 plane; it is
.

## Tangent

a trigonometric function. Its abbreviation is tan. The tangent of an acute angle in a right triangle is the ratio of the leg opposite the angle to the leg adjacent to the angle.

## tangent

[′tan·jənt]
(mathematics)
A line is tangent to a curve at a fixed point P if it is the limiting position of a line passing through P and a variable point on the curve Q, as Q approaches P.
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.

## tangent

Of lines, curves, and surfaces: meeting at a single point and having, at that point, the same direction.

## 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
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