A signal 2 Cos (150*pie*t+30) is sampled at 200 Hz . What will be the period of the discrete signal .S olve mathematically

Dear stuent 

Please find the below attachment suitable 

Fs = 200Hz , Frequency of sample 
F= 75 Hz (because omega = 2*pi*f*t, so it becomes 2*pi*75*t)
For converting into discrete signal
put t= nTs (Because sampling is done at sampling time of Ts for n times)
and Ts = 1/Fs, so above eqn becomes n/200
Original signal is
x(t)=2 cos (150*pi*t+30) substitute t =nTs and Ts by n/200
The answer of your Question will be following
x(n)=2 cos (2*pi*(75/200)*n+30)