Ask and Answer for Yasrudi ( trigonometri )

Ask #01 05 April 2017
Assalamu alaikum wr wb. Kak, mau tanya soal bab trigonometri. Soalnya seperti ini

$\textup{Nilai dari } cos\frac{2\pi }{7}+cos\frac{4\pi }{7}+cos\frac{6\pi }{7}\textup{ adalah}....$

Answer #01 05 April 2017

Waalaikum salam wr wb. Baik, kakak jawab.
$\\=cos\frac{2\pi }{7}+cos\frac{4\pi }{7}+cos\frac{6\pi }{7} \\ \\=\frac{2sin\frac{2\pi }{7}\left ( cos\frac{2\pi }{7}+cos\frac{4\pi }{7}+cos\frac{6\pi }{7} \right )}{2sin\frac{2\pi }{7}} \\ \\=\frac{2sin\frac{2\pi }{7}.cos\frac{2\pi }{7}+ 2cos\frac{4\pi }{7}.sin\frac{2\pi }{7} + 2cos\frac{6\pi }{7}.sin\frac{2\pi }{7}}{2sin\frac{2\pi }{7}} \\ \\=\frac{sin\frac{4\pi }{7}+ sin\frac{6\pi }{7}-sin\frac{2\pi }{7}+sin\frac{8\pi }{7}-sin\frac{4\pi }{7}}{2sin\frac{2\pi }{7}}, \\$
$\\=\frac{sin\frac{6\pi }{7}-sin\frac{2\pi }{7}+sin\frac{8\pi }{7}}{2sin\frac{2\pi }{7}} \\ \\=\frac{sin\frac{\pi }{7}-sin\frac{2\pi }{7}-sin\frac{\pi }{7}}{2sin\frac{2\pi }{7}} \\ \\=\frac{-sin\frac{2\pi }{7}}{2sin\frac{2\pi }{7}} \\ \\=-\frac{1}{2}$
Semoga bermanfaat

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