A sinusoidal signal is represented as
$$x(t) = \mathrm{cos}(\omega t) = \mathrm{cos}(2\pi f t)$$

$w$ is angular frequency and $f$ is frequency. See [Frequency definition][1]

Your signal $x(t) = 5 + 30\mathrm{cos}(2000\pi t) + 10\mathrm{cos}(6000\pi t) = 5\mathrm{cos}(2\pi \times 0 t) + 30\mathrm{cos}(2\pi \times 1000 t) + 10\mathrm{cos}(2\pi \times 3000 t)$

There are three frequencies $0, 1000, \textrm{ and } 3000\textrm{Hz}$ thus the bandwidth is $3000\textrm{Hz}$.


  [1]: https://en.wikipedia.org/wiki/Frequency