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



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eyust707
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well 5/12 = 3/12 + 2/12 right?

CheezeFace
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..Yeah

eyust707
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and
3/12 is 1/4
2/12 is 1/6

CheezeFace
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Mhm

CheezeFace
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I understand that far.. Kind of

eyust707
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sweet so that means that:
\[\tan ({5\pi \over 12} )= \tan ({3\pi \over 12} + {2\pi \over 12}) = \tan ({\pi \over 4} + {\pi \over 6})\]

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

eyust707
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Well then you can use an identity...

eyust707
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eyust707
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the bottom one should work

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

eyust707
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No its fine =) as long as you help me

eyust707
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what would you use for u?

eyust707
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what about v?

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

eyust707
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Yep! make sure you use (1/4)* pi\[\tan ({\pi \over 4} + {\pi \over 6})\]

eyust707
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u = \(\pi \over 4\)
v = \(\pi \over 6\)

eyust707
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we end up withdw:1354678186124:dw

eyust707
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tan(pi/4) = 1
tan(pi/6) = 1/sqrt(3)

CheezeFace
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Makes sense so far.

eyust707
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then substitute those numbers in

eyust707
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dw:1354678373033:dw

eyust707
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wait a minute.. something is isn't quite right

CheezeFace
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Erm, make the fractions rational?

eyust707
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the bottom + should actually be a 

eyust707
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dw:1354678613665:dw

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

eyust707
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@satellite73 whats the best way to simplify this?

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

CheezeFace
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..Um any break downs for it?..

UnkleRhaukus
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dw:1354711713075:dw

UnkleRhaukus
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dw:1354711757394:dw

UnkleRhaukus
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dw:1354711865053:dw