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.
sin 5x is equal to zero when:
5x = 0 or π
So given k as an arbitrary integer
5x = k π
So k can be: k = 0, 1, 2
x = k π/ 5
