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* + Δ*x*, *f*(*c* + Δ*x*)). Then the slope *m* of the secant line, through *P* and *Q*, is given by:

*x*approaches zero, this expression approaches the derivative of

*f*(

*c*), assuming a derivative exists.

See also: derivative, differential calculus