## anonymous one year ago 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!

1. anonymous

@ganeshie8 @Michele_Laino @zepdrix @Luigi0210 @Compassionate @Whitemonsterbunny17 @adrynicoleb @Xmoses1

2. Compassionate

$\sin \frac{ 11 \times 3.14 }{ 3 }$

3. Xmoses1

I wish i would have paid attention in high school...

4. anonymous

@Compassionate but how do I calculate it? I know the answer is sqrt(2)/2.

5. anonymous

@Compassionate I think there is a graph method, but I don't get it.

6. anonymous

7. Michele_Laino

hint: $\Large \frac{{11\pi }}{3} = 3\pi + \frac{{2\pi }}{3}$ then we have to use the formula of addition for "sin" function

8. anonymous

what is that?

9. anonymous

Is it sinacosb+sinbcosa?

10. Michele_Laino

yes! $\Large \begin{gathered} \sin \left( {\frac{{11\pi }}{3}} \right) = \sin \left( {3\pi + \frac{{2\pi }}{3}} \right) = \hfill \\ \hfill \\ = \sin \left( {3\pi } \right)\cos \left( {\frac{{2\pi }}{3}} \right) + \cos \left( {3\pi } \right)\sin \left( {\frac{{2\pi }}{3}} \right) = ...? \hfill \\ \end{gathered}$

11. anonymous

I don't really understand where to go from there.

12. Michele_Laino

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

13. anonymous

-sqrt(3)/2

14. Michele_Laino

hint: $\Large \begin{gathered} \sin \left( {\frac{{11\pi }}{3}} \right) = \sin \left( {3\pi + \frac{{2\pi }}{3}} \right) = \hfill \\ \hfill \\ = \sin \left( {3\pi } \right)\cos \left( {\frac{{2\pi }}{3}} \right) + \cos \left( {3\pi } \right)\sin \left( {\frac{{2\pi }}{3}} \right) = \hfill \\ \hfill \\ = 0 \cdot \left( { - \frac{1}{2}} \right) + \left( { - 1} \right) \cdot \left( {\frac{{\sqrt 3 }}{2}} \right) = ...? \hfill \\ \end{gathered}$

15. anonymous

yup, thanks for the help!

16. Michele_Laino

:)

17. anonymous

Hopefully I can ace the pop quiz if it is tomorrow! :D Now to sleep.

18. anonymous

$\sin(n\pi+\theta)=(-1)^n.\sin(\theta) \forall n \in \mathbb{Z}^+\mathbb{Z}^-$