## rudra333 2 years ago a math question

1. rudra333

$\cos ^{-1}(\sin \frac{ 11\pi }{ 6 })$

2. rudra333

@satellite73

3. rudra333

@satellite73 plz help

4. zugzwang

Play with the values for this one... Let $x = \cos^{-1}(\sin \frac{11\pi}{6})$and if we get the cosine of both sides, we are left with...$\cos x = \sin \frac{11\pi}{6}$perhaps it's simpler from here on in?

5. rudra333

6. zugzwang

seems like it

7. rudra333

@satellite73

8. zugzwang

You're right. Hang on... in general, $\cos(\frac{\pi}{2} - \theta)=\sin(\theta)$ So $\sin\frac{11\pi}{6}=\cos \left( \frac{\pi}{2}-\frac{11\pi}{6} \right)$ $=\cos \left( -\frac{8\pi}{6} \right)$ It would appear $x=-\frac{4\pi}{3}+2k\pi$ where k is any integer. But since we're talking angles, adding 360 degrees, or 2pi, would give the same angle. Consider doing that here, because that negative angle ain't pretty XD $x = -\frac{4\pi}{3}+2\pi=\frac{2\pi}{3}$

9. rudra333

k thanks but this other one is hard $\tan(\sin ^{-1}-\frac{ 5 }{ 13 }$

10. rudra333

)

11. zugzwang

It's a bit complicated, but think of it this way... the SINE of the angle is -5/13, so what is its TANGENT?

12. alanli123

here's what you do: sine of what angle will equal 5/13? Then you take that angle and take the tan of it.

13. rudra333

but i how do i do that?

14. alanli123

answer is 5/12 by the way

15. alanli123

|dw:1358823550014:dw|

16. alanli123

so... tan of theta is ?

17. rudra333

how did u get 12? and one is negative

18. alanli123

oops didn't catch the negative

19. alanli123

so if its negative then it means the angle is either in the third or fourth quadrant

20. alanli123

however my answer would still be correct if the angle was in the 3rd quadrant

21. rudra333

@zaynahf

22. rudra333

omg still confused

23. zaynahf

Im sorry, i dont know how to work this out.

24. rudra333

k :(

25. alanli123

did the problems include restrictions?

26. rudra333

yes

27. alanli123

what were they?

28. rudra333

but that's all the questions says

29. alanli123

?? so is there or is there no restrictions like 180<theta<270 (for exmaple)

30. alanli123

@satellite73 help!!

31. rudra333

no that is all the question says do u know the answer plz i am confused i will just do others if u don't know this

32. alanli123

alright... shoot gimme another question

33. rudra333

it is k i am doing graphing