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Find period of f(x) = cos(2x/3) - sin(4x/5)

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Given - f(x) = cos(2x/3) − sin(4x/5)

To Find - Period of the function

Solution - For cos(2x/3), period = $\frac{2π}{2/3}= 3π= \frac{6π}{2}$

For sin(4x/5), period = $\frac{2π}{4/5}= \frac{5π}{2}$

Now, take LCM of $\frac{5π}{2}$ and $\frac{6π}{2}$

LCM of 6 and 5 = 30

So, LCM = $\frac{30π}{2}= 15π$

Therefore, The period of f(x) = cos(2x/3) − sin(4x/5) is 15π

 

Posted by

Saniya Khatri

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