Secant of 30 Degrees
Theorem
- $\sec 30 \degrees = \sec \dfrac \pi 6 = \dfrac {2 \sqrt 3} 3$
where $\sec$ denotes secant.
Proof
| \(\ds \sec 30 \degrees\) | \(=\) | \(\ds \frac 1 {\cos 30 \degrees}\) | Secant is Reciprocal of Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {\frac {\sqrt 3} 2}\) | Cosine of $30 \degrees$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {2 \sqrt 3} 3\) | multiplying top and bottom by $2 \sqrt 3$ |
$\blacksquare$
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