11pi/6 is in 4th quadrant.
The reference angle is pi/6 because 11pi/6 is pi/6 radians away from 'x' axis.
In 4th quadrant, sin is negative and cos is positive, therefore tan is negative.
This means:
[tex]tan(\frac{11\pi}{6}) = -tan(\frac{\pi}{6}) = -\frac{sin(\pi/6)}{cos(\pi/6)} = -\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}[/tex]
