43,018 views
25 votes
25 votes
Evaluate the sine of the angle
0 = 4\pi / 30 is fada

User Sakshi Gatyan
by
2.6k points

1 Answer

15 votes
15 votes

By Compound Angles Theorem,


\begin{gathered} \sin ((4\pi)/(3))=\sin ((2\pi)/(3)+(2\pi)/(3))=2\sin ((2\pi)/(3))\cos ((2\pi)/(3))=2(\frac{\sqrt[]{3}}{2})(-(1)/(2))=-\frac{\sqrt[]{3}}{2} \\ \end{gathered}

Recall:


\begin{gathered} \sin ((2\pi)/(3))=\frac{\sqrt[]{3}}{2} \\ \\ \cos ((2\pi)/(3))=-(1)/(2) \end{gathered}

Hence, the correct answer is


-\frac{\sqrt[]{3}}{2}

User Nategoose
by
3.0k points
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