Secant of 345 Degrees

Theorem

$\sec 345 \degrees = \sec \dfrac {23 \pi} {12} = \sqrt 6 - \sqrt 2$

where $\sec$ denotes secant.


Proof

\(\ds \sec 345 \degrees\) \(=\) \(\ds \map \sec {360 \degrees - 15 \degrees}\)
\(\ds \) \(=\) \(\ds \sec 15 \degrees\) Secant of Conjugate Angle
\(\ds \) \(=\) \(\ds \sqrt 6 - \sqrt 2\) Secant of $15 \degrees$

$\blacksquare$


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
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.