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Tangent

: * For the tangent function see * [trigonometric functions] * . For other uses, see * [tangent (disambiguation)] * . *

In [geometry] , the ** tangent line ** (or simply the ** tangent ** ) to a [curve] at a given [point] is the [straight line] that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point. The same definition applies to [space curve] s and curves in * n * -dimensional [Euclidean space] .

Similarly, the ** tangent plane ** to a [surface] at a given point is the [plane] that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in [differential geometry] and has been extensively generalized; see [Tangent space] .

The word "tangent" comes from the Latin * tangere * , meaning "to touch".

** Tangent line to a curve **

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