Sine of 60 Degrees

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Theorem

$\sin 60 \degrees = \sin \dfrac \pi 3 = \dfrac {\sqrt 3} 2$

where $\sin$ denotes the sine function.


Proof

\(\ds \sin 60 \degrees\) \(=\) \(\ds \map \cos {90 \degrees - 60 \degrees}\) Cosine of Complement equals Sine
\(\ds \) \(=\) \(\ds \cos 30 \degrees\)
\(\ds \) \(=\) \(\ds \dfrac {\sqrt 3} 2\) Cosine of $30 \degrees$

$\blacksquare$


Sources

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