# Period of cos (5x+3) is ?

1
by namku
what is x here?
variable....like sinx cosx

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.

please click on the azur blue button Thanks above
sir,I should take tuition from u.
please click on the azur blue button Thanks above
ikr we shud take tution from sir