Cosine of 165 Degrees
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Theorem
- $\cos 165 \degrees = \cos \dfrac {11 \pi} {12} = - \dfrac {\sqrt 6 + \sqrt 2} 4$
where $\cos$ denotes cosine.
Proof
| \(\ds \cos 165 \degrees\) | \(=\) | \(\ds \map \cos {90 \degrees + 75 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\sin 75 \degrees\) | Cosine of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\dfrac {\sqrt 6 + \sqrt 2} 4\) | Sine 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