Cotangent of 120 Degrees
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Theorem
- $\cot 120 \degrees = \cot \dfrac {2 \pi} 3 = -\dfrac {\sqrt 3} 3$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 120 \degrees\) | \(=\) | \(\ds \map \cot {90 \degrees + 30 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\tan 30 \degrees\) | Cotangent of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\frac {\sqrt 3} 3\) | Tangent of 30 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