Why sin(0.2*x + pi) is aperiodic function? [closed]

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I know this might be too easy to be a question... but I can't get why sin(0.2*x + pi) is aperiodic?..

I tried to plot this in matlab and that's what I got:

That should be periodic right? Instead in "Schaum's Outline of Digital Signal Processing" book it says it's aperiodic

Answer 1

The function f(x) = sin(pi + 0.2*x) is periodic.

The sequence sin(pi + 0.2*n) where n=0, 1, ... is not periodic.

Answer 2

sin(0.2*x + pi), x in R (i.e. x - real) is periodic, as we could find such x0 that sin(0.2*x + pi) = sin(0.2*(x + x0) + pi)

sin(0.2*x + pi), x in N_0 (i.e. x - natural and zero) is not periodic. You've provided exactly the proof of that fact in page screenshot.