Given

x(t) = 3cos100πt

For a signal x(t) sampled with a sampling interval T_{s}, the discrete sequence can be written as

\(x(n) = x(t)|_{t=nT_s}\)

T_{s} = sampling interval

\(f_s = 75Hz\)

\(T_s = \frac 1{75}\)

\(x(n) = 3\cos 100\pi (\frac n{75})\)

\(x(n) = 3\cos (\frac{4\pi n}3)\)