What is the link between equation of a continuous signal versus equation of its sampled form?
The sequence $x[n]$ equals the continuous-time signal $x(t)$ sampled at $t=nT$, where $T=1/f_s$ is the sampling period:

$$x[n]=x(nT)=\cos(4000\pi nT)=\cos(4000\pi n/f_s)\tag{1}$$

So if $x[n]=\cos(n\pi/2)$ you just have to compare this argument to the argument in $(1)$ to figure out what $f_s$ is.

The normalized frequency of the discrete-time signal $x[n]$ is $\omega_0=\pi/2$ (in radians). It is related to the frequency $f$ in Hertz by

$$\omega_0=\frac{2\pi f}{f_s}$$