## anonymous 3 years ago Use a half-angle identity to find the evact value of each function. A.) Tan 165 degrees I have tried and cannot come up with the right answer. Can I have some help?

1. anonymous

Exact not evact sorry

2. tkhunny

2*165º = 330º = 360º - 30º Reference Angle -30º

3. anonymous

$\tan \left( \frac{x}{2} \right) = \frac{\sin x}{1 + \cos x}$ plug x = 330º

4. anonymous

i did that, and i checked the answer in the back and it did not go right. I messed up somewhere but i do not know where.

5. anonymous

maybe you forgot to rationalize the denominator?

6. tkhunny

Did you consider the quadrant? 330º is Quadrant IV (Tangent is Negative). 165º is Quadrant II (Tangent is negative) Please show your work and we'll be able to see where you wander off.

7. anonymous

|dw:1357957749155:dw|

8. tkhunny

@exraven wins. Just rationalize the denominator!

9. anonymous

how do you do that?

10. anonymous

multiply by the conjugate

11. anonymous

$\frac{-1}{2 +\sqrt{3}}$multiply by $\frac{2 -\sqrt{3}}{2 - \sqrt{3}}$

12. anonymous

the answer is square root 3 minus 2 in the book. I cannot quite get it to match

13. tkhunny

Again, let's see your work. We'll be able to tell where you wander off.

14. anonymous

|dw:1357958794041:dw|

15. anonymous

yes, what is the value of square root of 9?

16. anonymous

3

17. tkhunny

That's it. Don't panic that it does not yet match the book. Keep going!

18. anonymous

continue then

19. anonymous

|dw:1357959061747:dw|

20. anonymous

yes, you got it

21. anonymous

Thank you