Mathematics: Determine whether the function is periodic. if it is periodic, find the period. f(x) = 3 sin 2x + 4 cos 3x

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Determine whether the function is periodic. if

kendricklamar29

14.03.2022

$\frac{2\pi}{3}$

Step-by-step explanation:

We are given that a function

f(x)=3 sin 2x +4 cos 3x

We have to find that given function is periodic or not and if given function is periodic then find the period

We know that if a function is periodic then

f(x+c)=f(x)

We know that sin x and cos x are periodic function with period $2\pi$

Sum of periodic function is also periodic

Hence, given function is periodic function.

Period of sin x= $2\pi$

Then, $2 x=2\pi$

$x=\pi$

Period of cos x is $2\pi$

$3x=2\pi$

$x=\frac{2\pi}{3}$

$\frac{ lcm(\pi,2\pi}{lcm (1,3)}=\frac{2\pi}{3}$

Hence, period of given function is $\frac{2\pi}{3}$

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