Question

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

• A. $2\pi$
• B. $3\pi$
• C. $6\pi$
• D. $12\pi$

Answer 1

Answer: (D)

$12\pi$

Period of the function $f\left(x\right)=\sin \left(\frac{x}{3}\right)+\cos \left(\frac{x}{2}\right)$ is

L.C.M of periods of $\sin \left(\frac{x}{3}\right)$ and $\cos \left(\frac{x}{2}\right)$

$\Rightarrow$ L.C.M of $6\pi$ and $4\pi$ ($\because$ Periods of $\sin x$ and $\cos x$ is $2\pi$)

$\therefore$ Period of $f\left(x\right)$ is $12\pi$

Hence, option D.