Cotangent of 210 Degrees

Theorem

$\cot 210^\circ = \cot \dfrac {7 \pi} 6 = \sqrt 3$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 210^\circ\) \(=\) \(\ds \cot \left({360^\circ - 150^\circ}\right)\)
\(\ds \) \(=\) \(\ds -\cot 150^\circ\) Cotangent of Conjugate Angle
\(\ds \) \(=\) \(\ds \sqrt 3\) Cotangent of 150 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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