Secant of 30 Degrees

From ProofWiki
Jump to navigation Jump to search

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