Q. The period of the function $\sin\left( \frac{2x}{3} \right) + \sin\left( \frac{3x}{2} \right)$ is
A) $2\pi$
B) $10\pi$
C) $6\pi$
D) $12\pi$
Explanation
(d)
Period of $\sin\left( \frac{3x}{2} \right) = \frac{2\pi}{3/2} = \frac{4\pi}{3}$
And period of $\sin\left( \frac{2x}{3} \right) = \frac{2\pi}{2/3} = 3\pi$
$\therefore$ Period of $\sin{\left( \frac{2x}{3} \right) + \sin\left( \frac{3x}{2} \right) = \frac{LCM\ (3\pi,\ 4\pi)}{HCF\ (1,\ 3)}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 12\pi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.