## CheezeFace 2 years ago Help? D: How do you determine the exact trigonometric ratio of tan 5pi/12?

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1. eyust707

well 5/12 = 3/12 + 2/12 right?

2. CheezeFace

..Yeah

3. eyust707

and 3/12 is 1/4 2/12 is 1/6

4. CheezeFace

Mhm

5. CheezeFace

I understand that far.. Kind of

6. eyust707

sweet so that means that: $\tan ({5\pi \over 12} )= \tan ({3\pi \over 12} + {2\pi \over 12}) = \tan ({\pi \over 4} + {\pi \over 6})$

7. CheezeFace

That makes sense so far, it's usually what follows that ends up looking like Chinese. >.<

8. eyust707

Well then you can use an identity...

9. eyust707

10. eyust707

the bottom one should work

11. CheezeFace

Do you mind showing me how it would work out?.. >.< Sorry

12. eyust707

No its fine =) as long as you help me

13. eyust707

what would you use for u?

14. eyust707

15. CheezeFace

so u can be 1/4 and v can be 1/6

16. eyust707

Yep! make sure you use (1/4)* pi$\tan ({\pi \over 4} + {\pi \over 6})$

17. eyust707

u = $$\pi \over 4$$ v = $$\pi \over 6$$

18. eyust707

we end up with|dw:1354678186124:dw|

19. eyust707

tan(pi/4) = 1 tan(pi/6) = 1/sqrt(3)

20. CheezeFace

Makes sense so far.

21. eyust707

then substitute those numbers in

22. eyust707

|dw:1354678373033:dw|

23. eyust707

wait a minute.. something is isn't quite right

24. CheezeFace

Erm, make the fractions rational?

25. eyust707

the bottom + should actually be a -

26. eyust707

|dw:1354678613665:dw|

27. CheezeFace

OOOH. Right. Ohgawd. I'm so not ready for my test. lol

28. eyust707

@satellite73 whats the best way to simplify this?

29. CheezeFace

Lol..That's the step that keeps throwing me off.

30. CheezeFace

..Um any break downs for it?..

31. UnkleRhaukus

|dw:1354711713075:dw|

32. UnkleRhaukus

|dw:1354711757394:dw|

33. UnkleRhaukus

|dw:1354711865053:dw|