Cosine of 144 Degrees
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Theorem
- $\cos 144 \degrees = \cos \dfrac {4 \pi} 5 = -\dfrac \phi 2 = -\dfrac {1 + \sqrt 5} 4$
where $\cos$ denotes cosine.
Proof
| \(\ds \cos 144 \degrees\) | \(=\) | \(\ds \map \cos {180 \degrees - 36 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\cos 36 \degrees\) | Cosine of Supplementary Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\dfrac {1 + \sqrt 5} 4\) | Cosine of $36 \degrees$ |
$\blacksquare$