I really appreciate the help! How do I find sin(11pi/3)? I might have a pop quiz tomorrow and I really need help to figure this out. Thanks!

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I really appreciate the help! How do I find sin(11pi/3)? I might have a pop quiz tomorrow and I really need help to figure this out. Thanks!

Mathematics
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\[\sin \frac{ 11 \times 3.14 }{ 3 }\]
I wish i would have paid attention in high school...

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@Compassionate but how do I calculate it? I know the answer is sqrt(2)/2.
@Compassionate I think there is a graph method, but I don't get it.
Someone help please ;_;
hint: \[\Large \frac{{11\pi }}{3} = 3\pi + \frac{{2\pi }}{3}\] then we have to use the formula of addition for "sin" function
what is that?
Is it sinacosb+sinbcosa?
yes! \[\Large \begin{gathered} \sin \left( {\frac{{11\pi }}{3}} \right) = \sin \left( {3\pi + \frac{{2\pi }}{3}} \right) = \hfill \\ \hfill \\ = \sin \left( {3\pi } \right)\cos \left( {\frac{{2\pi }}{3}} \right) + \cos \left( {3\pi } \right)\sin \left( {\frac{{2\pi }}{3}} \right) = ...? \hfill \\ \end{gathered} \]
I don't really understand where to go from there.
it is simple, we have these values: \[\Large \begin{gathered} \sin \left( {3\pi } \right) = 0 \hfill \\ \cos \left( {\frac{{2\pi }}{3}} \right) = - \frac{1}{2} \hfill \\ \cos \left( {3\pi } \right) = - 1 \hfill \\ \sin \left( {\frac{{2\pi }}{3}} \right) = \frac{{\sqrt 3 }}{2} \hfill \\ \end{gathered} \] please substitute them into my formula above
-sqrt(3)/2
hint: \[\Large \begin{gathered} \sin \left( {\frac{{11\pi }}{3}} \right) = \sin \left( {3\pi + \frac{{2\pi }}{3}} \right) = \hfill \\ \hfill \\ = \sin \left( {3\pi } \right)\cos \left( {\frac{{2\pi }}{3}} \right) + \cos \left( {3\pi } \right)\sin \left( {\frac{{2\pi }}{3}} \right) = \hfill \\ \hfill \\ = 0 \cdot \left( { - \frac{1}{2}} \right) + \left( { - 1} \right) \cdot \left( {\frac{{\sqrt 3 }}{2}} \right) = ...? \hfill \\ \end{gathered} \]
yup, thanks for the help!
:)
Hopefully I can ace the pop quiz if it is tomorrow! :D Now to sleep.
\[\sin(n\pi+\theta)=(-1)^n.\sin(\theta) \forall n \in \mathbb{Z}^+\mathbb{Z}^-\]

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