Undefined

##csc(x) = 1/sin(x)## so

##csc(180) = 1/sin(180)= 1/0##. Because we’re dividing by 0 it is undefined.

To understand why this strange answer makes sense think about the unit circle:

graph{x^2+y^2=1 [-2.5 2.5 -1.25 1.25]}

If we tried to make a right triangle on the unit circle with points at the origin or ##(00)## and the point ##(10)## with an angle of 180 our third point would be ##(-10)##. This sad triangle would just be a line segment!

Cosecant is also used to find the ratio of hypotenuse/opposite side of a right triangle. The opposite side of this triangle doesn’t exist so we call this cosecant undefined.