Checking if a Discrete Time Signal is Periodic

Question

I am trying to figure out if the following discrete time signal is periodic.

$$ x[n]=\sin((6\pi/7)n+1) $$

I know that

A DT signal x[n] is periodic if there exists a positive integer N such that $$x[n+N] = x[n], \forall n\in Z$$

However, I am having trouble figuring out where to begin.

I found this other question, but I am not sure they are considering that the signal is discrete: Is signal periodic? What is the period? since the period is $7/3$, a non-integer value.

Plotting the function in mathematic shows that the period is around 7.

Thanks.

Edit: Added plot

Answer 1

To find the fundamental period of:

$$x[n] = \sin((6\pi/7)n+1)$$

First we set $(6\pi/7)n = 2\pi$

Then we solve for n to get: $n = 7/3$

Since this is a discrete signal, we need the period to be an integer so, we multiply by 3 to get it to the nearest integer.

Hence, the fundamental period is $7$