Cotangent of 345 Degrees

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
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