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

Think of the tangent problems backward.

so

.

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