Here we are to find the values of x in which the function
f (x) = csc 5x is discontinuous. What this usually means is to find when the
value approaches infinity.
We know from trigonometric identities that csc is the
equivalent to 1 / sin, therefore the function in terms of sin is:
f(x) = 1 / sin 5x
We can see that the function becomes discontinuous when sin
5x = 0, that is a value divided by 0 is discontinuous or approaches infinity.