Definition:Secant
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Definition
Trigonometry
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.
Analysis
Real Function
Let $x \in \R$ 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.
