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Math Help - Ahhh tan! Easy question for you guys

  1. #1
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    Ahhh tan! Easy question for you guys

    Ok...

    how is the tan of \frac{\pi}{6} = \frac{\sqrt3}{3}

    I am extremely confused.

    Thanks guys.
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  2. #2
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    Draw an equilateral triangle of side length 2 sitting on its base.
    Split it down the middle.
    You now have a 60/30/90 triangle. The base is 1 (half of the original 2), the hypotenuse is 2 (the original side). Pythagoras's rule says the other side is sqrt(3).
    Remember that 30 degrees is pi/6 radians.
    Use tan A = opp/adj to get tan (pi/6) = 1/sqrt(3).
    Rationalise the denominator of this fraction by mutiplying top and bottom by sqrt(3) to get....voila.... sqrt(3) / 3.
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  3. #3
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    Thank you! All you had to remind me of was the 1/sqrt(3) and it finally popped into my head.

    However, is there another way to get the 1 that is in the numerator? Like... without doing the triangle stuff? Cause in my head... tan = y/x

    In this case, y is 1/2. That is why I was confused..

    WOW DUH...

    1/2 divided by sqrt(3)/2....... the two's would cancel and you'd have 1/sqrt(3)

    I'm dumb. lol
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