Question

The period of $f\left(x\right)=\sin \frac{2\pi x}{3}+\cos \frac{\pi x}{2}$ is?

• A. $3$
• B. $4$
• C. $6$
• D. $12$

Answer 1

The correct option is D $12$

Given : $f\left(x\right)=\sin \frac{2\pi x}{3}+\cos \frac{\pi x}{2}$

Since, $\sin \frac{2\pi x}{3}$ and $\cos \frac{\pi x}{2}$ are periodic functions with periods $\frac{2\pi }{2\pi /3}=3$ and $\frac{2\pi }{\pi /2}=4$, respectively.
Therefore, $\sin \frac{2\pi x}{3}+\cos \frac{\pi x}{2}$ is periodic with period equal to LCM of $3$ and $4$, i.e., $12$.

Hence, $f\left(x\right)$ is periodic with period $12$.