Answer:
[tex]\frac{2\pi}{3}[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=3 sin 2x +4 cos 3x[/tex]
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
[tex]f(x+c)=f(x)[/tex]
We know that sin x and cos x are periodic function with period [tex]2\pi[/tex]
Sum of periodic function is also periodic
Hence, given function is periodic function.
Period of sin x=[tex]2\pi[/tex]
Then, [tex]2 x=2\pi[/tex]
[tex]x=\pi[/tex]
Period of cos x is [tex]2\pi[/tex]
[tex]3x=2\pi[/tex]
[tex]x=\frac{2\pi}{3}[/tex]
[tex]\frac{ lcm(\pi,2\pi}{lcm (1,3)}=\frac{2\pi}{3}[/tex]
Hence, period of given function is [tex]\frac{2\pi}{3}[/tex]
