In the following problems find the fundamental period of signals and determine periodicity.

(a) Find the fundamental period of the following signals, and verify it

(i) x(t) = cos(t + π/4),                                      

(ii) y(t) = 2 + sin(2π t),                 

(iii) z(t) = 1 + (cos (t)/sin(3t))

(b) The signal x₁(t) is periodic of fundamental period T₀, and the signal y₁(t) is also periodic of fundamental period 10T₀. Determine if the fo-lowing signals are periodic, and if so give their fundamental periods

(i) z₁ (t) = x₁ (t) + 2y₁ (t)                                

(ii) v₁(t) = x₁(t)/y₁ (t)                      

(iii) w₁ (t) = x(t) + y₁ (10 t)