Cotangent of 240 Degrees
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Theorem
- $\cot 240^\circ = \cot \dfrac {4 \pi} 3 = \dfrac {\sqrt 3} 3$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 240^\circ\) | \(=\) | \(\ds \cot \left({360^\circ - 120^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\cot 120^\circ\) | Cotangent of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sqrt 3} 3\) | Cotangent of 120 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