Cosine of 285 Degrees
Theorem
- $\cos 285^\circ = \cos \dfrac {19 \pi} {12} = \dfrac {\sqrt 6 - \sqrt 2} 4$
where $\cos$ denotes cosine.
Proof
| \(\ds \cos 285^\circ\) | \(=\) | \(\ds \cos \left({360^\circ - 75^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 75^\circ\) | Cosine of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sqrt 6 - \sqrt 2} 4\) | Cosine 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