Sine of 330 Degrees

Theorem

$\sin 330 \degrees = \sin \dfrac {11 \pi} 6 = -\dfrac 1 2$

where $\sin$ denotes the sine function.


Proof

\(\ds \sin 330 \degrees\) \(=\) \(\ds \map \sin {360 \degrees - 30 \degrees}\)
\(\ds \) \(=\) \(\ds -\sin 30 \degrees\) Sine of Conjugate Angle
\(\ds \) \(=\) \(\ds -\dfrac 1 2\) Sine 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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