The period of the function sin left( frac{2x} | vedclass

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(D) The period of $\sin \left( \frac{2x}{3} \right)$ is $T_1 = \frac{2\pi}{2/3} = 3\pi$. The period of $\sin \left( \frac{3x}{2} \right)$ is $T_2 = \f

Vedclass · Accepted Answer

$12$

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(D) The period of $\sin \left( \frac{2x}{3} \right)$ is $T_1 = \frac{2\pi}{2/3} = 3\pi$. The period of $\sin \left( \frac{3x}{2} \right)$ is $T_2 = \frac{2\pi}{3/2} = \frac{4\pi}{3}$. The period of the sum of two periodic functions is the $L.C.M.$ of their individual periods. We need to find the $L.C.M.$ of $3\pi$ and $\frac{4\pi}{3}$. $L.C.M. \left( \frac{a}{b}, \frac{c}{d} \right) = \frac{L.C.M.(a, c)}{H.C.F.(b, d)}$. $L.C.M. \left( \frac{3\pi}{1}, \frac{4\pi}{3} \right) = \frac{L.C.M.(3\pi, 4\pi)}{H.C.F.(1, 3)} = \frac{12\pi}{1} = 12\pi$. Thus, the period is $12\pi$.

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

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