Tangent of 330 Degrees

Theorem

$\tan 330^\circ = \tan \dfrac {11 \pi} 6 = -\dfrac {\sqrt 3} 3$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 330^\circ\) \(=\) \(\ds \tan \left({360^\circ - 30^\circ}\right)\)
\(\ds \) \(=\) \(\ds -\tan 30^\circ\) Tangent of Conjugate Angle
\(\ds \) \(=\) \(\ds -\frac {\sqrt 3} 3\) Tangent of 30 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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