The solution set of (5+4 cos theta)(2 cos the | vedclass

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(C) Given the equation: $(5+4 \cos 	heta)(2 \cos 	heta+1)=0$Since $5+4 \cos 	heta$ can never be $0$ (because $-1 \le \cos 	heta \le 1$,so $1 \le 5

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$\left\{\frac{2 \pi}{3}, \frac{4 \pi}{3}\right\}$

Vedclass · Answer

(C) Given the equation: $(5+4 \cos 	heta)(2 \cos 	heta+1)=0$Since $5+4 \cos 	heta$ can never be $0$ (because $-1 \le \cos 	heta \le 1$,so $1 \le 5+4 \cos 	heta \le 9$),we must have:$2 \cos 	heta + 1 = 0$$\cos 	heta = -\frac{1}{2}$In the interval $[0, 2\pi]$,the values of $	heta$ for which $\cos 	heta = -\frac{1}{2}$ are:$	heta = \pi - \frac{\pi}{3} = \frac{2\pi}{3}$ and $	heta = \pi + \frac{\pi}{3} = \frac{4\pi}{3}$Thus,the solution set is $\left\{\frac{2\pi}{3}, \frac{4\pi}{3}ight\}$.

The solution set of $(5+4 \cos \theta)(2 \cos \theta+1)=0$ in the interval $[0, 2\pi]$ is:

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