A. csc x=-5/2. sin x=1/csc x=-2/5. Since pi<x<3/2pi, this angle is in the third quadrant. cos x must also be negative, we can narrow the answer choices down to A and D. cos x=-\sqrt(1-sin^2 x)=-\sqrt(21)/5. tan x=(-2/5)/(-\sqrt(21)/5)=2/\sqrt(21), so the answer is A.