Question

Find the period of the following funciton:

$\sin \frac{2\pi x}{3}+\cos \frac{\pi x}{2}$,

Answer 1

Period of $\sin \frac{2\pi x}{3}=\frac{2\pi }{\lambda }=\frac{2\pi }{2\pi /3}=3$

Period of $\cos \frac{\pi x}{2}=\frac{2\pi }{\lambda }=\frac{2\pi }{\pi /2}=4$

$\therefore$ Period of $f+g$ is L.C.M. of $3$ and $4$ i.e. $12$.