f(x) = 64 + 27cos(2pi/365(x+145))

what would be the period

i tried by solving 2pi/(2pi/365)

period = 365 but this doesn't seem right

No that would be right. When you divide by a fraction it is the same as multiplying by the reciprocal. so it would be 2pi x 365/2pi

so it would be 2pi365/2pi and they would cancel out.
Plus the equation is set up for a yearly period anyway. 365 is the period of days