Cotangent of 300 Degrees

Theorem

$\cot 300 \degrees = \cot \dfrac {5 \pi} 3 = - \dfrac {\sqrt 3} 3$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 300 \degrees\) \(=\) \(\ds \map \cot {360 \degrees - 60 \degrees}\)
\(\ds \) \(=\) \(\ds -\cot 60 \degrees\) Cotangent of Conjugate Angle
\(\ds \) \(=\) \(\ds -\frac {\sqrt 3} 3\) Cotangent of $60 \degrees$

$\blacksquare$


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.