For each of the discrete signals below, determine whether they are periodic or not. Calculate the periods of those that are periodic.

(a) \(x(n)=\cos ^{2}\left(\frac{2 \pi}{15} n\right)\)

(b) \(x(n)=\cos \left(\frac{4 \pi}{5} n+\frac{\pi}{4}\right)\)

(c) \(x(n)=\cos \left(\frac{\pi}{27} n+31\right)\)

(d) \(x(n)=\sin (100 n)\)

(e) \(x(n)=\cos \left(\frac{11 \pi}{12} n\right)\)

(f) \(x(n)=\sin [(5 \pi+1) n]\).