What is the period of the function of f(x) =  cos 1/2x and the period of the function of f(x) = tan3x?

aruv | Student

If there exist smallest T>0 such that f(x+T)=f(x) then T is known as period of f.

Thus

f(x)=cos(x/2)

f(x+T)=cos((x+T)/2)

But f(x)=f(x+T)

cos(x/2)=cos(x/2+T/2)

This implies

T/2=2pi

T=4pi

and

f(x)=tan(3x)

f(x+T)=tan(3(x+T))=tan(3x+3T)

but

3T=pi

T=pi/3

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