Encyclopedia > Secant

  Article Content

Secant

In trigonometry, a secant is a particular trigonometric function, the reciprocal of the cosine function.


A secant line of a curve is that line which intersects two (or more) points upon the curve. Note that this use of "secant" comes from the Latin "secare", for "to cut"; this is not a reference to the trigonometric function.

It can be used to approximate the tangent to a curve, at some point P. If the secant to a curve is defined by two points, P and Q, with P fixed and Q variable, as Q approaches P along the curve, the direction of the secant approaches that of the tangent at P (assuming there is just one).

As a consequence, one could say that the limit of the secant's slope, or direction, is that of the tangent.

Secant Approximation

Consider the curve defined by y = f(x) in a Cartesian coordinate system, and consider a point P with coordinates (c, f(c)) and another point Q with coordinates (c + Δx, f(c + Δx)). Then the slope m of the secant line, through P and Q, is given by:

m = Δy / Δx = [f(c + Δx) - f(c)] / [(c + Δx) - c] = [f(c + Δx) - f(c)] / Δx

The righthand side, of the above equation, is a variation of Newton's difference quotient. As Δx approaches zero, this expression approaches the derivative of f(c), assuming a derivative exists.

See also: derivative, differential calculus



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
East Farmingdale, New York

... 102.8 males. For every 100 females age 18 and over, there are 100.6 males. The median income for a household in the town is $68,125, and the median income for a family ...

 
 
 
This page was created in 30.4 ms