Cosecant of Zero

Theorem

$\csc 0$ is undefined

where $\csc$ denotes cosecant.

Proof

From Cosecant is Reciprocal of Sine:

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

From Sine of Zero is Zero:

$\sin 0 = 0$

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

$\blacksquare$

Also see

• Sine of Zero is Zero
• Cosine of Zero is One
• Tangent of Zero
• Cotangent of Zero
• Secant of Zero

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