# Why the value of sin120 equal to sin60?

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Nghi N. Share
Feb 17, 2017

There are many ways to prove that sin 60 = sin 120.
1. By unit circle.
On the unit circle, the arc ${60}^{\circ}$ and the arc ${120}^{\circ}$ have the same sin value $\left(\frac{\sqrt{3}}{2}\right)$.
2. By Table of special arcs:
On the Table --> $\sin 60 = \sin 120 = \frac{\sqrt{3}}{2}$
3. By trig identity:
sin 2a = 2sina.cos a
sin 120 = 2sin 60.cos 60.
Trig table gives $\cos 60 = \frac{1}{2}$, there for sin 120 = sin 60

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