frequency domain representation

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moonnightingale

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If i am having a signal

cos (4000*pi*t)
and i have to represent in frequency domain
then is this solution correct:-

since
omega =2*Pi*f
so 2*pi*f = 4000* Pi

f=2000

so it means that frequnecy of our signal is 2000 Hz

now i can plot it this way
 

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The Fourier Transform (Or frequency domain representation ) of Cos(2*pi*f0*t) is 0.5*( delta(f-f0)+delta(f+f0)). If you want to represent it graphically, Conventionally it is shown by two arrows at +f0 and -f0.
P.S: delta(x) is the dirac function.
 

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