Cotangent of 150 Degrees
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Theorem
- $\cot 150 \degrees = \cot \dfrac {5 \pi} 6 = -\sqrt 3$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 150 \degrees\) | \(=\) | \(\ds \map \cot {90 \degrees + 60 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\tan 60 \degrees\) | Cotangent of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\sqrt 3\) | Tangent 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