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  4. The period of the function f(x)= sin ( sin (x/5) ) is

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Q. The period of the function $ f(x)=\sin \left( \sin \frac{x}{5} \right) $ is

Bihar CECEBihar CECE 2014

Solution:

Given, $ f(x)=\sin \left( \sin \frac{x}{5} \right) $ $ \therefore $ $ f(x+10\pi )=\sin \left[ \sin \left( \frac{x+10\pi }{5} \right) \right] $ $ =\sin \left[ \sin \left( \frac{x}{5}+2\pi \right) \right] $ $ =\sin \left( \sin \frac{x}{5} \right)=f(x) $ Hence, period of $ f(x) $ is $ 10\pi $