Cosecant of Three Right Angles

Theorem

$\csc 270 \degrees = \csc \dfrac {3 \pi} 2 = -1$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 270 \degrees\) \(=\) \(\ds \map \csc {360 \degrees - 90 \degrees}\)
\(\ds \) \(=\) \(\ds -\csc 90 \degrees\) Cosecant of Conjugate Angle
\(\ds \) \(=\) \(\ds -1\) Cosecant of Right Angle

$\blacksquare$


Also see


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.