The period of the function f(theta) = sin fra | vedclass

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(D) The period of $\sin(a	heta)$ is $\frac{2\pi}{|a|}$ and the period of $\cos(b	heta)$ is $\frac{2\pi}{|b|}$.For $f(	heta) = \sin \frac{	heta}{3}

Vedclass · Accepted Answer

$12$

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(D) The period of $\sin(a	heta)$ is $\frac{2\pi}{|a|}$ and the period of $\cos(b	heta)$ is $\frac{2\pi}{|b|}$.For $f(	heta) = \sin \frac{	heta}{3} + \cos \frac{	heta}{2}$,the period of $\sin \frac{	heta}{3}$ is $T_1 = \frac{2\pi}{1/3} = 6\pi$.The period of $\cos \frac{	heta}{2}$ is $T_2 = \frac{2\pi}{1/2} = 4\pi$.The period of the sum $f(	heta)$ is the least common multiple $(LCM)$ of $T_1$ and $T_2$.$LCM(6\pi, 4\pi) = 12\pi$.Therefore,the period of the function is $12\pi$.

The period of the function $f(\theta) = \sin \frac{\theta}{3} + \cos \frac{\theta}{2}$ is (in $\pi$)

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