[tex] \frac{7 \pi }{6} [/tex] is in the 3rd quadrant... (It is also 210 degrees)
To find the reference angle (which is the distance to the x-axis)
[tex] \frac{7 \pi }{6} - \pi = \frac{ \pi }{6} [/tex] (or 30 degrees)
sin [tex] \frac{ \pi }{6} = \frac{1}{2} [/tex]
