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cos (5pi/12) => exact value

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    is there a way for me to work out cos (5pi/12) without using the cos-graph but only the "magic triangle" ?
    thanks!
  2. Offline

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    What in the world is the magic triangle?
  3. Offline

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    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.
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    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
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    Well, cos2A = 2cos²A - 1.

    Let A = 5pi/12.

    cos(5pi/6) = 2cos²(5pi/12) - 1.

    Can you take it from here?
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    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.

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