Definition:Cosecant
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Definition
Trigonometry
In the above right triangle, we are concerned about the angle $\theta$.
The cosecant of $\angle \theta$ is defined as being $\dfrac{\text{Hypotenuse}} {\text{Opposite}}$.
Thus it is seen that the cosecant is the reciprocal of the sine.
Analysis
Real Function
Let $x \in \C$ be a real number.
The real function $\csc x$ is defined as:
- $\csc x = \dfrac 1 {\sin x}$
where $\sin x$ is the sine of $x$.
The definition is valid for all $x \in \R$ such that $\sin x \ne 0$.
Complex Function
Let $z \in \C$ be a complex number.
The complex function $\csc z$ is defined as:
- $\csc z = \dfrac 1 {\sin z}$
where $\sin z$ is the sine of $z$.
The definition is valid for all $z \in \C$ such that $\sin z \ne 0$.
