Imagine the unit circle. A point (x, y) has coordinates $\displaystyle (cos(\theta), sin(\theta))$. As the angle gets smaller and smaller the point on the unit circle gets closer and closer to (1, 0). Which means that $\displaystyle cos(0) = 1$ and $\displaystyle sin(0) = 0$.Originally Posted by>_<SHY_GUY>_<

Think of the tangent problems backward.

$\displaystyle tan \left ( \frac{\pi}{6} \right ) = \frac{\sqrt{3}}{3}$

so

$\displaystyle tan^{-1} \left ( \frac{\sqrt{3}}{3} \right ) = \frac{\pi}{6}$.

The other inverse tangent problems follow a similar logic.

The 30 - 60 - 90 triangle contains a 30 degree angle. tan(30) = sqrt(3) / 3. You are thinking of either sin(60) or cos(30), which are both sqrt(3) / 2.

-Dan