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Help? D: How do you determine the exact trigonometric ratio of tan 5pi/12?

Trigonometry
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well 5/12 = 3/12 + 2/12 right?
..Yeah
and 3/12 is 1/4 2/12 is 1/6

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Other answers:

Mhm
I understand that far.. Kind of
sweet so that means that: \[\tan ({5\pi \over 12} )= \tan ({3\pi \over 12} + {2\pi \over 12}) = \tan ({\pi \over 4} + {\pi \over 6})\]
That makes sense so far, it's usually what follows that ends up looking like Chinese. >.<
Well then you can use an identity...
1 Attachment
the bottom one should work
Do you mind showing me how it would work out?.. >.< Sorry
No its fine =) as long as you help me
what would you use for u?
what about v?
so u can be 1/4 and v can be 1/6
Yep! make sure you use (1/4)* pi\[\tan ({\pi \over 4} + {\pi \over 6})\]
u = \(\pi \over 4\) v = \(\pi \over 6\)
we end up with|dw:1354678186124:dw|
tan(pi/4) = 1 tan(pi/6) = 1/sqrt(3)
Makes sense so far.
then substitute those numbers in
|dw:1354678373033:dw|
wait a minute.. something is isn't quite right
Erm, make the fractions rational?
the bottom + should actually be a -
|dw:1354678613665:dw|
OOOH. Right. Ohgawd. I'm so not ready for my test. lol
@satellite73 whats the best way to simplify this?
Lol..That's the step that keeps throwing me off.
..Um any break downs for it?..
|dw:1354711713075:dw|
|dw:1354711757394:dw|
|dw:1354711865053:dw|

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