operatorname{Arg}left(sin frac{6 pi}{5}+ileft | vedclass

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(D) Let $Z = \sin \frac{6 \pi}{5} + i(1 + \cos \frac{6 \pi}{5})$.Using trigonometric identities $\sin 2	heta = 2\sin	heta\cos	heta$ and $1 + \cos 2

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$\frac{9 \pi}{10}$

Vedclass · Answer

(D) Let $Z = \sin \frac{6 \pi}{5} + i(1 + \cos \frac{6 \pi}{5})$.Using trigonometric identities $\sin 2	heta = 2\sin	heta\cos	heta$ and $1 + \cos 2	heta = 2\cos^2	heta$ with $	heta = \frac{3\pi}{5}$:$Z = 2\sin \frac{3\pi}{5}\cos \frac{3\pi}{5} + i(2\cos^2 \frac{3\pi}{5})$$Z = 2\cos \frac{3\pi}{5} (\sin \frac{3\pi}{5} + i\cos \frac{3\pi}{5})$Since $\frac{3\pi}{5} = \frac{\pi}{2} + \frac{\pi}{10}$,we have $\sin \frac{3\pi}{5} = \cos \frac{\pi}{10}$ and $\cos \frac{3\pi}{5} = -\sin \frac{\pi}{10}$.$Z = 2\cos \frac{3\pi}{5} (\cos \frac{\pi}{10} - i\sin \frac{\pi}{10})$$Z = 2\cos \frac{3\pi}{5} (\cos(-\frac{\pi}{10}) + i\sin(-\frac{\pi}{10}))$Since $\cos \frac{3\pi}{5} < 0$,the argument is $\pi - \frac{\pi}{10} = \frac{9\pi}{10}$.

$\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=$

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