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Math Help - tan(pi/8)

  1. #1
    Junior Member
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    Oct 2005
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    54

    tan(pi/8)

    Anyone got any leads on solving:
    <br />
tan(\frac{\pi}{8})<br />
    Last edited by a4swe; October 7th 2005 at 01:01 AM.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Solve? You mean looking it up on a calculator is not enough?
    Anyway, my calculator here says tan(pi/8) = 0.414213562.

    Or, maybe, you mean this, (one of many ways):
    tan(pi/8) = tan[(pi/4)/2]
    We know the trig functions value of pi/4 (or 45 degrees) without bothering to consult a clculator, so, maybe this is what you mean by "solve for tan(pi/8).

    Okay. Then we know also this trig identity:
    tan(A/2) = (1 -cosA)/sinA = sinA/(1 +cosA) ----***

    If A = pi/4, then without calculator, we can solve for tan(A/2).

    tan(pi/8)
    = tan[(pi/4)/2]
    = [1 -cos(pi/4)]/[sin(pi/4)]
    = [ 1 -1/sqrt(2)]/[1/sqrt(2)]
    = in the end, sqrt(2) -1
    = 1.4142... -1
    = 0.4142.....

    Or,
    tan(pi/8)
    = [sin(pi/4)]/[1 +cos(pi/4)]
    = sqrt(2) -1
    = 0.4142....
    Last edited by ticbol; October 7th 2005 at 01:43 AM.
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  3. #3
    Junior Member
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    Oct 2005
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    Yep, like that.
    Thanks.
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