Determine minimum sample rate for continuous sinusoid Consider a signal $$ x(t) = \cos(175\pi t) $$ which is sampled to produce discrete time signal $$ x[n] = x(nT_s) $$ The fundamental period of $x[n]$ is $$ N_0 = 7 $$

Given this, what is the smallest possible sample rate $T_s$? (Ans: 1.6327 ms).

I would assume that this is related to finding the Nyquist frequency. I was thinking:

Since, $$N_0 = 7 \implies f_0 = \frac17 \implies f_{\mathrm{Nyquist}} = 2 \frac17\implies T_s = \frac72 $$ However, this is obviously incorrect. I am not even using any information of the original signal. Any suggestions on what I could be doing wrong here?
Remember that the cosine function repeats itself every $2\pi$. The discrete signal can be written as $$x(n)=\cos(175\pi n T_s)$$

So when the argument reaches $2\pi$, we'll have a period. As we know that the fundamental period is $7$, then

$$175\pi \cdot7T_s=2\pi \implies T_s =\frac{2}{7\cdot 175}=1.6327\cdot 10^{-3}$$