Cotangent of 285 Degrees

Theorem

$\cot 285 \degrees = \cot \dfrac {19 \pi} {12} = -\paren {2 - \sqrt 3}$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 285 \degrees\) \(=\) \(\ds \cot \paren {360 \degrees - 75 \degrees}\)
\(\ds \) \(=\) \(\ds -\cot 75^\circ\) Cotangent of Conjugate Angle
\(\ds \) \(=\) \(\ds -\paren {2 - \sqrt 3}\) Cotangent of $75 \degrees$

$\blacksquare$


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
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