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  4. The period of f(x)= sin (2π x/3)+ cos (π x/2) is

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Q. The period of $ f(x)=\sin \frac{2\pi x}{3}+\cos \frac{\pi x}{2} $ is

Bihar CECEBihar CECE 2015

Solution:

Since, $ \sin \frac{2\pi x}{3} $ and $ \cos \frac{\pi x}{2} $ are periodic functions with periods $ \frac{2\pi }{2\pi /3}=3 $ and $ \frac{2\pi }{\pi /2}=4, $ respectively. Therefore, $ f(x) $ is periodic with period and equal to LCM of 3 and 4, i.e. 12.