Recall that the reciprocal of the csc function is the sin function, which is an odd function. The angle -pi/6 has its terminal side in Quadrant 4, for which the opposite side is negative, important in determining the sign of csc(-pi/6).
sin(-pi/6) = - sin(pi/6) = -1/2.
Thus, csc(-pi/6) = -1 / (-1/2), or +2 (answer)
