Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f (x) at a point x = c on the curve if the line passes through the point (c, f (c)) on the curve and has slope f '(c) where f ' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.

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.

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Tangent (disambiguation)

A tangent, in geometry, is a straight line through a point on a curve that has the same direction at that point as the curve.

Tangent may also refer to:

Mathematics

  • Analogous concepts for surfaces and higher-dimensional smooth manifolds, such as the tangent space
    • More generally, in geometry, two curves are said to be tangent when they intersect at a given point and have the same direction at that point; see for instance tangent circles
    • Bitangent, a line that is tangent to two different curves, or tangent twice to the same curve
  • More generally, in geometry, two curves are said to be tangent when they intersect at a given point and have the same direction at that point; see for instance tangent circles
  • Bitangent, a line that is tangent to two different curves, or tangent twice to the same curve
  • The tangent function, one of the six basic trigonometric functions

    • Music

  • Tangent (clavichord), a part of the action of the clavichord that both initiates and sustains a tone, and helps determine pitch
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    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Tangent_(disambiguation)

    Trigonometric functions

    In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

    The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.

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    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Trigonometric_functions

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    Tangent

    by: Beth Orton

    Lost myself in a tangent of words
    Can't decide what I've seen or heard
    Can't sleep for counting sheep
    How long...does this river..run deep?
    How long...does this river..run deep?
    Building 'em up in order to find
    What's not lost but left behind
    My instinct got bruised, but I still see
    I was a victim of being no casualty
    Just like coming home...just like coming home
    Just like coming home...felt just like coming home
    They say that you weave deadly tricks
    Cantrip to the worldly hicks
    Stare cold with dull surprise
    Spark evil to hell in every tear you cry...every tear you cry
    Building 'em up in order to find
    What's not lost but left behind
    My instinct got bruised, but I still see
    I was a victim of being no casualty
    Just like coming home...just like coming home
    Just like coming home...felt just like coming home
    Cut off my toes to spite my feet
    Drank your poison, didn't taste too sweet
    Saw the heavens in my mind
    And it's there...for me...to find.
    Oh it's there...for me...to find
    Building 'em up in order to find
    What's not lost but left behind
    My instinct got bruised, but I still see
    I was a victim of being no casualty
    Just like coming home...just like coming home
    Just like coming home...felt just like coming home
    Lost myself in a tangent
    Lost myself in a tangent
    Lost myself in a tangent




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