If sin theta = -1/3 and 180 < theta < 270 what is tan theta?

##tantheta = 1/sqrt(8) = sqrt(8)/8##
Because theta is greater than 180 and less than 270 you know this is a 3rd quadrant triangle. So I have included a 3rd quadrant triangle. They tell you that ##sintheta = -1/3##
Because ##sintheta## is equal to opposite/hypotenuse you can draw a triangle as follows:
Now use to find the adjacent side:
##(-1)^2 + (adjacent)^2 = 3^2##
##1 + (adjacent)^2 = 9##
##(adjacent)^2 = 8##
##sqrt(adjacent^2) = +-sqrt(8)##
Because this is a 3rd quadrant triangle we choose the negative root:
##adjacent = -sqrt(8)##
We’re almost done. ##tantheta = (opposite)/(adjacent)##
Thus ##tantheta = -1/-sqrt(8) = 1/sqrt(8) = sqrt(8)/8##