Sine of 300 Degrees

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Theorem

$\sin 300 \degrees = \sin \dfrac {5 \pi} 3 = -\dfrac {\sqrt 3} 2$

where $\sin$ denotes the sine function.


Proof

\(\ds \sin 300 \degrees\) \(=\) \(\ds \map \sin {360 \degrees - 60 \degrees}\)
\(\ds \) \(=\) \(\ds -\sin 60 \degrees\) Sine of Conjugate Angle
\(\ds \) \(=\) \(\ds -\dfrac {\sqrt 3} 2\) Sine of $60 \degrees$

$\blacksquare$


Sources