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i don't know how to solve, please help me!
y = a cos (bx + c) + d
y = a sin (bx + c) + d
… the period is 2pi/b or 360/b.
for (i),
y = cos [(1/2)x + pi/3] + pi
period = 2pi/(1/2) = 4pi
for (ii),
apply double angle formula …
y = (cos 2x)^2
= (1/2) cos 4x + 1/2
period = 2pi/(4) = (1/2)pi