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CheezeFace

  • 3 years ago

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

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  1. eyust707
    • 3 years ago
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    well 5/12 = 3/12 + 2/12 right?

  2. CheezeFace
    • 3 years ago
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    ..Yeah

  3. eyust707
    • 3 years ago
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    and 3/12 is 1/4 2/12 is 1/6

  4. CheezeFace
    • 3 years ago
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    Mhm

  5. CheezeFace
    • 3 years ago
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    I understand that far.. Kind of

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

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

  8. eyust707
    • 3 years ago
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    Well then you can use an identity...

  9. eyust707
    • 3 years ago
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    1 Attachment
  10. eyust707
    • 3 years ago
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    the bottom one should work

  11. CheezeFace
    • 3 years ago
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    Do you mind showing me how it would work out?.. >.< Sorry

  12. eyust707
    • 3 years ago
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    No its fine =) as long as you help me

  13. eyust707
    • 3 years ago
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    what would you use for u?

  14. eyust707
    • 3 years ago
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    what about v?

  15. CheezeFace
    • 3 years ago
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    so u can be 1/4 and v can be 1/6

  16. eyust707
    • 3 years ago
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    Yep! make sure you use (1/4)* pi\[\tan ({\pi \over 4} + {\pi \over 6})\]

  17. eyust707
    • 3 years ago
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    u = \(\pi \over 4\) v = \(\pi \over 6\)

  18. eyust707
    • 3 years ago
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    we end up with|dw:1354678186124:dw|

  19. eyust707
    • 3 years ago
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    tan(pi/4) = 1 tan(pi/6) = 1/sqrt(3)

  20. CheezeFace
    • 3 years ago
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    Makes sense so far.

  21. eyust707
    • 3 years ago
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    then substitute those numbers in

  22. eyust707
    • 3 years ago
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    |dw:1354678373033:dw|

  23. eyust707
    • 3 years ago
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    wait a minute.. something is isn't quite right

  24. CheezeFace
    • 3 years ago
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    Erm, make the fractions rational?

  25. eyust707
    • 3 years ago
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    the bottom + should actually be a -

  26. eyust707
    • 3 years ago
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    |dw:1354678613665:dw|

  27. CheezeFace
    • 3 years ago
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    OOOH. Right. Ohgawd. I'm so not ready for my test. lol

  28. eyust707
    • 3 years ago
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    @satellite73 whats the best way to simplify this?

  29. CheezeFace
    • 3 years ago
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    Lol..That's the step that keeps throwing me off.

  30. CheezeFace
    • 3 years ago
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    ..Um any break downs for it?..

  31. UnkleRhaukus
    • 3 years ago
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    |dw:1354711713075:dw|

  32. UnkleRhaukus
    • 3 years ago
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    |dw:1354711757394:dw|

  33. UnkleRhaukus
    • 3 years ago
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    |dw:1354711865053:dw|

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