Cosine of 345 Degrees
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Theorem
- $\cos 345 \degrees = \cos \dfrac {23 \pi} {12} = \dfrac {\sqrt 6 + \sqrt 2} 4$
where $\cos$ denotes cosine.
Proof
| \(\ds \cos 345 \degrees\) | \(=\) | \(\ds \map \cos {360 \degrees - 15 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 15 \degrees\) | Cosine of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sqrt 6 + \sqrt 2} 4\) | Cosine 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