In the relation $x=\cos (\text{ω}t+kx),$the dimensions of  $\text{ω}$ are

Given,

Here, $(\text{ω}t+kx)$ is an angle so the dimension of

 Or dimensions of $\text{ω}t=\left[{\text{M}}^0{\text{L}}^0{\text{T}}^0\right]$

 Or dimensions of $\text{ω}=\frac{\left[{\text{M}}^0{\text{L}}^0{\text{T}}^0\right]}{\left[\text{T}\right]}$

Or $=\left[{\text{M}}^0{\text{L}}^0{\text{T}}^{-1}\right]$