I like to imagine a triangle in place of the negative x axis of the unit circle where the opposite side = 0, the adjacent is -1 and the hypotenuse = 1.
so sin 180 = 0/1 = 0, cos 180 = -1/1 = -1 and tan 180 = -0/-1 = 0.
Then the other ratios are csc is 1/0 = indeterminate, sec = 1/-1 = -1 and cot is indeterminate.