Cotangent of 165 Degrees
Jump to navigation
Jump to search
Theorem
- $\cot 165 \degrees = \cot \dfrac {11 \pi} {12} = -\paren {2 + \sqrt 3}$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 165 \degrees\) | \(=\) | \(\ds \map \cot {90 \degrees + 75 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\tan 75 \degrees\) | Cotangent of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\paren {2 + \sqrt 3}\) | Tangent of $75 \degrees$ |
$\blacksquare$
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