Cosecant of Full Angle

Theorem

$\csc 360 \degrees = \csc 2 \pi$ is undefined

where $\csc$ denotes cosecant.

Proof

From Cosecant is Reciprocal of Sine:

$\csc \theta = \dfrac 1 {\sin \theta}$

From Sine of Full Angle:

$\sin 360 \degrees = 0$

Thus $\csc \theta$ is undefined at this value.

$\blacksquare$

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles