Finding original signal, given signal obtained by sampling

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The discussion focuses on reconstructing the continuous-time signal x(t) from the discrete-time signal x(n) = 3.9 cos(0.80πn + 0.2π), sampled at 578.4 samples/sec. Participants express confusion about determining the original frequencies from the sampled signal. A breakthrough reveals the relationship between the sampling frequency and the original frequency, calculated as fo = 231.36 Hz. The possible frequencies are identified as fo ± fs*k, where k is an integer. The conversation emphasizes understanding the relationship between sampling and frequency in signal processing.
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Let, x(n) = 3.9 cos(0.80πn + 0.2π) be the discrete-time signal obtained by sampling a continuous-time signal x(t) at a sampling rate of 578.4 samples/sec. Find possible expressions for x(t).

Hey all,
I am quiet unfamiliar with this type of question, and haven't been able to put anything together that makes sense.
I know that the amplitude and phase will stay the same, however figuring out possible frequencies has got me stuck. Would greatly appreciate anyone that is able to walk me through or point me in the right direction for this problem. Thanks in advance!
 
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Just had a breakthrough, needed to get away from the problem and then look at it again.
Just in case anyone wants to correct me:
-2*pi*fo/fs = 0.8*pi
-Therefore fo = 231.36
-Therfore possible frequencies are fo +-fs*k where k is an integer
 

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