Question

The period of following function: $f\left(x\right)=\left[\sin 3x\right]+|\cos 6x|$ is $\frac{a\pi }{9}$. Find $a$.
(Note : $[.]$ denotes the greatest integer function)

Answer 1

$f\left(x\right)=\left[\sin 3x\right]+|\cos 6x|$
Period of $\left[\sin 3x\right]$ is $\frac{2\pi }{3}$ and period of $|\cos 6x|$ is $\frac{\pi }{6}$
$\Rightarrow$ Period of $f\left(x\right)$ is $=$ L.C.M of $\frac{2\pi }{3}$ and $\frac{\pi }{6}=\frac{2\pi }{3}$
$\therefore a=6$