Cosecant of 30 Degrees

Theorem

$\csc 30^\circ = \csc \dfrac \pi 6 = 2$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 30^\circ\) \(=\) \(\ds \frac 1 {\sin 30^\circ}\) Cosecant is Reciprocal of Sine
\(\ds \) \(=\) \(\ds \frac 1 {\frac 1 2}\) Sine of $30^\circ$
\(\ds \) \(=\) \(\ds 2\) multiplying top and bottom by $2$

$\blacksquare$


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
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