Cosecant of Zero
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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
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