## anonymous one year ago Check my work if I'm correct. Find the exact value of sin(-11pi/12).

1. anonymous

So I changed it from radians to degrees to make it easier.

2. hybrik

sin(-11(3.1415926535)/12)

3. anonymous

I'm not allowed to use the calculator. :)

4. hybrik

= sin(0.26)

5. hybrik

math I just remember first digits of pi so

6. hybrik

You would just simplify 3.141592/12, which is around 0.26

7. hybrik

then find the sin of 0.26

8. anonymous

Should I use a reference angle to find -165?

9. anonymous

So it'll be 15.

10. anonymous

|dw:1438110805222:dw|

11. anonymous

$= -(\sin60\cos45-\cos60\sin45)$

12. Nnesha

i would change negative angle to positive and then use one of de formula

13. Nnesha

i like positive stuff :D

14. anonymous

|dw:1438110888230:dw|

15. anonymous

|dw:1438110954725:dw|

16. anonymous

I don't know if I did it right, so what do you guys think?

17. Nnesha

gimme a sec

18. anonymous

All right. :)

19. Nnesha

okay so i add 360 int -165 360 -165 =195 i used sin(a+b) formula $\huge\rm sin(a+b) =\sin A \times \cos B + \cos A \times \sin B$ $\sin(45+150) =\sin 45 \cos 150 + \cos 45 \times \sin 150$ $\sin(45+150) =\frac{ \sqrt{2} }{ 2} \times \frac{ -\sqrt{3} }{ 2 }+\frac{ \sqrt{2} }{ 2 }\times \frac{ 1 }{ 2 }$ and got $\frac{ -\sqrt{6} + \sqrt{2 }}{ 4}$ so your answer is correct :D

20. anonymous

Thank you! :)

21. Nnesha

gO_Od job! i almost forgot these stuff ;D

22. freckles

the cool thing about these is your start doesn't have to match someone elses start that like I would have done it this way: $\sin(\frac{-11\pi}{12}) \\ \text{ sine function is odd } \\ -\sin(\frac{11\pi}{12}) \\ -\sin(165^o) \\ -\sin(120^o+45^o) \\ -[\sin(120^o)\cos(45^o)+\sin(45^o) \cos(120^o)] \\ -[\frac{\sqrt{3}}{2} \frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} \frac{-1}{2}] \\ -[\frac{\sqrt{6}}{4}-\frac{\sqrt{2}}{4}] \\ -[\frac{\sqrt{6}-\sqrt{2}}{4}] \\ \text{ distribute outside negative } \\ \frac{-\sqrt{6}--\sqrt{2}}{4} \\ \frac{-\sqrt{6}+\sqrt{2}}{4}$

23. Nnesha

yeah but i wasn't sure that we can take out negative sign $\sin(\frac{ -11\pi }{ 2 }) --> -\sin(\frac{ 11\pi }{ 2 })$

24. Nnesha

ik sin(-x)=-sin(x) hmm so that's possible

25. freckles

right and if we had cos(-x) then this is just cos(x) since cos is even

26. freckles

that is for example $\cos(\frac{-11\pi}{12})=\cos(\frac{11\pi}{12})$

27. Nnesha

true :=)