# Thread: Ahhh tan! Easy question for you guys

1. ## 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.

2. 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.

3. 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