Question

The period of the function $\sin\left( \frac{3x}{2} \right)$is.

• A. $= \frac{2\pi}{3/2} = \frac{4\pi}{3}$
• B. $3\pi$
• C. $\frac{4\pi}{3}$
• D. $12\pi$

Answer 1

Answer: (D)

$12\pi$

Answer 2

Period of $\sin \left( \frac { 2 x } { 3 } \right) = \frac { 2 \pi } { 2 / 3 } = 3 \pi$

Period of $\sin \left( \frac { 3 x } { 2 } \right) = \frac { 2 \pi } { 3 / 2 } = \frac { 4 \pi } { 3 }$

L.C.M. of $3 \pi$ and $\frac { 4 \pi } { 3 }$= $12 \pi$. Hence period is $12 \pi$.