Cosecant of 30 Degrees
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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