The period of the function ( 2x 3 ) + ( 3x 2 ) is - Vidyadip

MCQ

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 $
✓
$12\pi $

✓

Answer

Correct option: D.

$12\pi $

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

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

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

Hence period is $12\pi $.

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