Cosecant is Reciprocal of Sine

Theorem
Let $\theta$ be an angle such that $\sin \theta \ne 0$.

Then:
 * $\csc \theta = \dfrac 1 {\sin \theta}$

where $\csc$ and $\sin$ mean cosecant and sine respectively.

Proof
Let a point $P = \tuple {x, y}$ be placed in a cartesian plane with origin $O$ such that $OP$ forms an angle $\theta$ with the $x$-axis.

Then:

When $\sin \theta = 0$, $\dfrac 1 {\sin \theta}$ is not defined.