## anonymous one year ago if sin theta equals -5/13 pi is less than theta less than 3 pi/2 find cos theta over 2 This is just all over the place

1. anonymous

If $$\sin \theta = -\frac{ 5 }{ 13 }, \pi<\theta<\frac{ 3\pi }{ 2 }$$, find $$\cos \frac{ \theta }{ 2 }$$. this?

2. anonymous

haha yes!

3. anonymous

you need to use the half angle identity $\cos \theta = \pm \sqrt{\frac{ 1+\cos \theta }{ 2}}$ which means you need to find cos Θ.

4. anonymous

Where are you suppose to use the sin theta part then?

5. anonymous

Θ is in the 3rd quadrant so cos Θ is negative, and you can use the pythagorean theorem/triples to find it

6. anonymous

Right so its 5 12 13 triangle what would you use for the cos theta part?

7. anonymous

yes

8. anonymous

so cos Θ would be -12/13

9. anonymous

make sense?

10. anonymous

So then you would just solve after?

11. anonymous

right

12. anonymous

Alright lets see how this works working it out then I might show you the work to see if its correct lol

13. anonymous

@peachpi Like this?

14. anonymous

I can't really see if the 12/13 is negative. If it is then you're right and you just have to simplify it

15. anonymous

Alright yeah its negative sorry its hard to tell but we got sqrt of 1 over 26?

16. anonymous

that's what I got. Then since Θ is in the third quadrant, Θ/2 is in the second where cos is negative so got with -√(1/26)

17. anonymous

or -(√26)/26 if you have to rationalize

18. anonymous

but I don't think either of them are right becauase the answer has to be greater then pi and less then 3 pi over 2?

19. anonymous

that's a restriction on Θ. That's how we know Θ is in the 3rd quadrant.|dw:1436551969316:dw|

20. anonymous

the question is asking for cos (Θ/2), not Θ itself

21. anonymous

The answer is simple, A true saiyan sprinkles when he tinkles.

22. anonymous

Wait so whats the answer then? im so confused lmaoo

23. anonymous

I just said it

24. anonymous

cos (Θ/2) = -√(1/26)

25. anonymous

Is there a way to check the answer itself?

26. anonymous

try wolframalpha.com not sure how you'd have to word it though

27. anonymous

28. anonymous

yes

29. anonymous

Alright I have an exam coming up which is why I am asking these questins XD haha thank you!

30. anonymous

you're welcome