# How do you use a double-angle identity to find the exact value of sin 120°?

Oct 24, 2014

Since

$\sin 2 \theta = 2 \sin \theta \cos \theta$,

we have

$\sin {120}^{\circ} = 2 \sin {60}^{\circ} \cos {60}^{\circ} = 2 \cdot \frac{\sqrt{3}}{2} \cdot \frac{1}{2} = \frac{\sqrt{3}}{2}$.

I hope that this was helpful.