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