The period of |2sin 3theta + 4cos 3theta | is | vedclass

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(D) Let $f(	heta) = 2\sin 3	heta + 4\cos 3	heta$. We can write this as $f(	heta) = R\sin(3	heta + \alpha)$,where $R = \sqrt{2^2 + 4^2} = \sqrt{20

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$\frac{\pi}{3}$

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(D) Let $f(	heta) = 2\sin 3	heta + 4\cos 3	heta$. We can write this as $f(	heta) = R\sin(3	heta + \alpha)$,where $R = \sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5}$. So,$f(	heta) = 2\sqrt{5} \sin(3	heta + \alpha)$. The function given is $g(	heta) = |f(	heta)| = |2\sqrt{5} \sin(3	heta + \alpha)|$. The period of $\sin(3	heta + \alpha)$ is $T = \frac{2\pi}{3}$. The period of $|\sin(3	heta + \alpha)|$ is $\frac{T}{2} = \frac{2\pi/3}{2} = \frac{\pi}{3}$. Thus,the period of $|2\sin 3	heta + 4\cos 3	heta |$ is $\frac{\pi}{3}$.

The period of $|2\sin 3\theta + 4\cos 3\theta |$ is

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