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2015-05-01T13:02:42+05:30

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Cos (x) = cos [ (2π) n + x ]    for all x ∈ R  ,  n ∈ Z  (all integers)        ---- (1)
           So 2π is the period of  Cos x

f (x )  =  f (n T + x),  for all x ∈ R  and n ∈ Z      --- (2)
                     then T is the period

let 5 x + 3 = X        and    let  x = n T + x

Cos X = Cos (5 x + 3)
         =  Cos [ 5 (n T + x) + 3 ]
         =  Cos [ 5 n T + 5 x + 3 ]
         = Cos [ n 5 T  + X ]            compare this with  (1)

 5 T =  2 π            =>    T = 2 π / 5 

What this means is that  Cos X  repeats itself every 2 π  radians or 360 deg.  and,  the function  Cos (5x+3)  repeats itself  every  2 π / 5 radians or  144 deg.

2 5 2
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