Verified answer

Use half-angle identity...

tan(x/2) = sin(x)/(1 + cos(x))

Let x = π/3. Then...

tan((π/3)/2) = sin(π/3)/(1 + cos(π/3))

= √(3)/2/(1 + ½)

= √(3)/2/(3/2)

= √(3)/2 * 2/3

= √(3)/3

I hope this helps!

You draw a right triangle with hypot = 1, and two legs of 1/2 and sqrt3/2. The two acute angles will be π/6 and π/3.

Now you can find the exact values of the six basic trig functions for these two angles.

the tan of pie over 6 is the same as the sin of pie over 6 divided by the cos of pie over six. I also hope you know that you're dealing with radians here and not degrees, if you want a helpful cheat sheet on these matters go look up the "Unit Circle" if you use that you'll have it

That's because it's (1/rt3)

Set up an appropriate angle to see why, or use series expansion.

Look up the series expansion of tan. It'll tell you how to do it

tan(t) =>

sin(t)/cos(t)

tan(pi/6) =>

sin(pi/6) / cos(pi/6) =>

(1/2) / (sqrt(3) / 2) =>

1 / sqrt(3) =>

sqrt(3) / 3