Question

List the discontinuities for the function f(x) = cot( 5x/3 ).

Answer 1

`x=(3\pi n)/(5)`

Explanation:

We know that
`cot((5x)/(3))=(cos((5x)/(3)))/(sin((5x)/(3)))`, so
`cot((5x)/(3))` is undefined where
`sin((5x)/(3))=0`:

`sin((5x)/(3))=0\\\\(5x)/(3)=\pi n\\\\5x=3\pi n\\\\x=(3\pi n)/(5)`

So, the discontinuities for the function
`f(x)=cot((5x)/(3))` are where
`x=(3\pi n)/(5)` with
`n` being any integer.