Determine the period

Given the function f(x)=cos(x-30°) for x[-360°;360°]

 

Determine the period of the function g if g(x)=f(2x)
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g(x)=cos(2x-30). When 2x-30=0, x=15 and g(15)=1; when 2x-30=90, x=60 and g(60)=0; when 2x-30=180, x=105 and g(105)=-1; when 2x-30=270, x=150 and g(150)=0; when 2x-30=360, x=195 and g(195)=1=g(15), so the period is 195-15=180.

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