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 $\dfrac{\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:


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

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:


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

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.