Definition:Secant Function

Trigonometry

 * SineCosine.png

In the above right triangle, we are concerned about the angle $$\theta$$.

The secant of $$\angle \theta$$ is defined as being $$\frac{\text{Hypotenuse}} {\text{Adjacent}} $$.

Thus it is seen that the secant is the reciprocal of the cosine.

Real Function
Let $$x \in \C$$ be a real number.

The real function $$\sec x$$ is defined as:


 * $$\sec x = \frac 1 {\cos x}$$

where:
 * $$\cos x$$ is the cosine of $$x$$.

The definition is valid for all $$x \in \R$$ such that $$\cos x \ne 0$$.

Complex Function
Let $$z \in \C$$ be a complex number.

The complex function $$\sec z$$ is defined as:


 * $$\sec z = \frac 1 {\cos z}$$

where:
 * $$\cos z$$ is the cosine of $$z$$.

The definition is valid for all $$z \in \C$$ such that $$\cos z \ne 0$$.

Linguistic Note
The word secant comes from the Latin word for to cut.

Also see

 * Sine, cosine, tangent, cotangent and cosecant.