Prove f(x) = sin(x^2) isn't periodic. f is periodic if f(x + t) = f(x) for all x in f's domain. I know about 1 way of proving it by derivative and boundedness but is this another way? If f is periodic then sin(x^2) = sin((x + t)^2) Finding t: (I don't know the proper way of doing this, maybe I ought to add + 2kpi) x^2=x^2 +2xt + t^2 (I could square root it but it's the same) t(t + 2x) = 0 t1 = 0 or t2 = -2x t > 0 so t1 isn't. t(x) = -2x, but t can't be dependant on x, as it needs to be constant, so t2 isn't a solutio . So I have proved the hipothesis.