Definition:Cosecant

Trigonometry

 * SineCosine.png

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.

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 $\sin z \ne 0$.

Also see

 * Sine, cosine, tangent, cotangent and secant.