Cosecant of 345 Degrees

Theorem

$\csc 345 \degrees = \csc \dfrac {23 \pi} {12} = -\paren {\sqrt 6 + \sqrt 2}$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 345 \degrees\) \(=\) \(\ds \map \csc {360 \degrees - 15 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 15 \degrees\) Cosecant of Conjugate Angle
\(\ds \) \(=\) \(\ds -\paren {\sqrt 6 + \sqrt 2}\) Cosecant 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.