Sine of 144 Degrees
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Theorem
- $\sin 144 \degrees = \cos \dfrac {4 \pi} 5 = \sqrt {\dfrac 5 8 - \dfrac {\sqrt 5} 8}$
where $\sin$ denotes sine.
Proof
| \(\ds \sin 144 \degrees\) | \(=\) | \(\ds \sin \paren {180 \degrees - 36 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sin 36 \degrees\) | Sine of Supplementary Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sqrt {\dfrac 5 8 - \dfrac {\sqrt 5} 8}\) | Sine of $36 \degrees$ |
$\blacksquare$