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: For the tangent function see [trigonometric functions] . For other uses, see [tangent (disambiguation)] .
Tangent to a curve
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

At each point, the line is always tangent to the curve. Its slope is the derivative; the positivity, negativity and zeroes of the derivative are marked by green, red and black respectively.

A tangent, a chord, and a secant to a circle

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