Sine of 285 Degrees
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Theorem
- $\sin 285^\circ = \sin \dfrac {19 \pi} {12} = - \dfrac {\sqrt 6 + \sqrt 2} 4$
where $\sin$ denotes the sine function.
Proof
\(\ds \sin 285^\circ\) | \(=\) | \(\ds \sin \left({360^\circ - 75^\circ}\right)\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds - \sin 75^\circ\) | Sine of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds - \dfrac {\sqrt 6 + \sqrt 2} 4\) | Sine of $75^\circ$ |
$\blacksquare$
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