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Find the value of trigonometry

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the exact value of cos 247o+sin 293o


    2. Relevant equations
    trigonometry identities


    3. The attempt at a solution
    The furthest I can get is:

    cos 247o+sin 293o
    = cos 247o - cos 23o
    = -2 sin 135o sin 112o
    = -√2 cos 22o

    Then stuck....
     
  2. jcsd
  3. Dec 7, 2013 #2

    tiny-tim

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    hi independent! :smile:
    erm :redface: … 203 ? :wink:

    hint: always subtract from 360° (if necessary), to get an angle less than 180° ! :smile:
     
  4. Dec 7, 2013 #3
    247 = 270 - 23

    293 = 270 + 23

    cos (270 - 23) = ?
    sin (270 + 23) = ?
     
  5. Dec 8, 2013 #4
    Hi independent?? :rofl:

    Sorry I don't think I get your hint. cos 23o = - cos 203o. So
    cos 247o + cos 203o
    = 2 cos 225ocos 22o
    = -√2 cos 22o


    cos (270 - 23) = - sin 23o
    sin (270 + 23) = - cos 23o

    So:
    - sin 23o - cos 23o
    = - sin 23o - sin 67o
    = -2 sin 45o cos 22o
    = - √2 cos 22o

    All lead to - √2 cos 22o. Maybe it is me doing it the wrong way but I don't know how to manipulate the question in other way to give a better result

    Thanks
     
  6. Dec 9, 2013 #5

    tiny-tim

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    hi songoku! :smile:

    (sorry about the typo! :biggrin:)
    ah, i didn't see that :redface:
    yes, that's the best you can do

    (btw, i'd have done cos247 + sin293 = cos113 - sin67 = -cos67 - sin67 = -√2cos22 …

    Chestermiller's :smile: way of course is also fine, but i'm not as familiar with cos and sin of 270° as he is, so i'd be afraid of making a mistake! :redface:)

    i'l guess that when the question said "exact", it just meant "compact" o:)
     
  7. Dec 9, 2013 #6

    haruspex

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    Had it said cos 247o+cos 293o there would have been an exact answer. (Note what the two angles add up to.) Misprint perhaps?
     
  8. Dec 10, 2013 #7
    Maybe misprint. Thanks a lot for all the help :smile:
     
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