Cosine of 255 Degrees
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Theorem
- $\cos 255^\circ = \cos \dfrac {17 \pi} {12} = - \dfrac {\sqrt 6 - \sqrt 2} 4$
where $\cos$ denotes cosine.
Proof
\(\ds \cos 255^\circ\) | \(=\) | \(\ds \cos \left({360^\circ - 105^\circ}\right)\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \cos 105^\circ\) | Cosine of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds - \frac {\sqrt 6 - \sqrt 2} 4\) | Cosine of 105 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