cos (5pi/12) => exact value

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  1. gioms's Avatar
    1 10-06-2007  16:55
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    cos (5pi/12) => exact value
    is there a way for me to work out cos (5pi/12) without using the cos-graph but only the "magic triangle" ?
    thanks!
  2. Swayum's Avatar
    2 10-06-2007  16:57
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    Re: cos (5pi/12) => exact value
    What in the world is the magic triangle?
  3. Rabite's Avatar
    3 10-06-2007  17:08
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    Re: cos (5pi/12) => exact value
    Use the angles pi/4 and pi/6.
    Not sure what a magic triangle is...you shouldn't need to resort to any magic to solve this one.
  4. gioms's Avatar
    4 10-06-2007  17:13
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    • Location: Germany
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    Re: cos (5pi/12) => exact value
    I meant the triangles where you can easily read the cos,sines of etc in surd form..
    sorry, I dont quite understand your hint with the pi/4 pi/6 idea?
    thanks again
  5. Simba's Avatar
    5 10-06-2007  17:26
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    Re: cos (5pi/12) => exact value
    Well, cos2A = 2cos²A - 1.

    Let A = 5pi/12.

    cos(5pi/6) = 2cos²(5pi/12) - 1.

    Can you take it from here?
  6. Rabite's Avatar
    6 10-06-2007  17:26
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    Re: cos (5pi/12) => exact value
    http://artpad.art.com/?jjfhnudcxw

    That's the triangle. Dunno if it's your magic one.
    But you're looking to find the lengths cosAcosB and sinAsinB.

    [edit]
    Well, fine. If you're going to do it the normal way, you might as well just say
    5/12 = 1/4+1/6 and cos(A+B) = cosAcosB-sinAsinB.
    Last edited by Rabite; 10-06-2007 at 17:27.
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