List discontinuities for function

Question

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

Question options:

1)	n(  ), where n is an integer
2)	n(  ), where n is an integer
3)	n(  ), where n is an integer
4)	There are no discontinuities.

Answer 1

The cotangent function is undefined when sinθ = zero since cot = 1/tan and tan = sin/cos. sinθ is 0 at θ = 0, π, 2π,....which is all integer multiples of π.

So wherever 7x/3 = nπ, the cot(7x/3) will be undefined and thus discontinuous; Let 7x/3 = nπ, so x = 3nπ/7 for all integer values of n.