First thing to do is to change the radians to degrees so it's easier to determine our angle and where it lies in the coordinate plane. [tex] \frac{7 \pi }{6} * \frac{180}{ \pi }=210 [/tex]. If we sweep out a 210 degree angle, we end up in the third quadrant, with a 30 degree angle. In this quadrant, x and y are both negative, but the hypotenuse, no matter where it is, will never ever be negative. So the side across from the 30 degree reference angle is -1, and the hypotenuse is 2, so the sine of this angle, opposite over hypotenuse, is -1/2
