Cotangent of 345 Degrees
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Theorem
- $\cot 345 \degrees = \cot \dfrac {23 \pi} {12} = -\paren {2 + \sqrt 3}$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 345 \degrees\) | \(=\) | \(\ds \map \cot {360 \degrees - 15 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\cot 15 \degrees\) | Cotangent of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\paren {2 + \sqrt 3}\) | Cotangent of $15 \degrees$ |
$\blacksquare$
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