Sine of 345 Degrees
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Theorem
- $\sin 345^\circ = \sin \dfrac {23 \pi} {12} = - \dfrac {\sqrt 6 - \sqrt 2} 4$
where $\sin$ denotes the sine function.
Proof
| \(\ds \sin 345^\circ\) | \(=\) | \(\ds \sin \left({360^\circ - 15^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds - \sin 15^\circ\) | Sine of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds - \dfrac {\sqrt 6 - \sqrt 2} 4\) | Sine 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