Cosine of 18 Degrees
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Theorem
- $\cos 18 \degrees = \cos \dfrac \pi {10} = \dfrac {\sqrt {10 + 2 \sqrt 5} } 4$
where $\cos$ denotes the cosine function.
Proof
| \(\ds \cos 18 \degrees\) | \(=\) | \(\ds \map \cos {90 \degrees - 72 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sin 72 \degrees\) | Cosine of Complement equals Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sqrt {10 + 2 \sqrt 5} } 4\) | Sine of $72 \degrees$ |
$\blacksquare$